CN109685728A - Digital image processing method based on local time-frequency domain conversation - Google Patents
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Abstract
The present invention relates to a kind of digital image processing methods based on local time-frequency domain conversation, comprising: obtains digital picture low-pass filter and high-pass filter using discrete wavelet analysis method；Acquisition denoising data image signal is filtered by low-pass filter and high-pass filter to noisy data image signal to be processed；Using soft or hard wavelet threshold, to treated, data image signal carries out second denoising processing.The present invention can solve the problems, such as mixed Gaussian and impulsive noise image denoising using mixing nonlinear smoothing filter and single threshold value wavelet filtering combination.
Description
Technical field
The invention belongs to image and signal processing technology field more particularly to a kind of numbers based on local time-frequency domain conversation
Image processing method.
Background technique
Due to current big data, cloud is shared and Internet of Things situation is grown rapidly, to information integration, software development and application,
The technologies such as Multi-media image processing improve requirements at the higher level, and people are for useful information (picture, different-format in real life
Encoded video) capture status also become increasingly conspicuous, normally due to image collection is to the transmission stage, due to picture catching environment or
The reasons such as electronic component device usually can make image be doped into the high-frequency signals such as many noises, dirt, to reduce picture
Quality and whole visual perception；This " false image " is caused to judge by accident so that receiving end subscriber.So this is specially
Benefit is exactly directed to the image containing noise and carries out denoising early period and signal enhancing, compression scheduling algorithm Optimal flattening analysis, after being
Continuous image segmentation, image restoration provide basis early period, and then reach user and use best promising result.
It is different in Digital Image Transmission process (image border texture, spike and low-and high-frequency signal distributions) characteristic, usually can
Image raw information is interfered, useful information in picture " being flooded " or " hiding " can be made.For traditional Denoising Algorithm,
Although value filtering can effectively remove the noise in noise image, quality eliminates certain specific details in image while improvement,
Image is caused to become chaos；In terms of nonlinear smoothing filter is usually used in impulsive noise, when the degree that is disturbed is bigger, filtering
Effect is not significant, the equally meeting tiny node loss of image, and image quality decrease.Above two filtering is in the intrinsic processing of details
On show slightly shortcoming.
Currently, time-frequency domain-wavelet transformation becomes one of engineering discipline research hot topic direction and field；Also to calculating mathematics
Cause unprecedentedly to cause a sensation with calculus field.It covers linear topological mapping, Fourier reconciles and divides as Mathematics Discipline subdiscipline
All various aspects such as analysis, curved surface lines construction, difference coefficient value theory；Especially identified, originally in digital signal extraction, image texture characteristic
Body Semantic mapping, machine intelligence vision and non-linear diagnosis and calculating field have very prominent application.It analyzes base in Fourier
Space and frequency partial transformation are carried out to energy signal function on plinth, are embodied in translation and flexible, can objective reality it is anti-
It reflects and effectively transfers out by multi-scale refinement problem in image or voice；Solve conventional Fourier function microcosmic angle not
The problem of can solve.Furthermore, it is possible to segment time window function by low frequency transform；Function is changed over time ground wink by high frequency
State process is presented one by one, i.e. signals transmission removal noise pollution and fine impurities suspended particulate, can real-time and precise assurance times
Meaning variations in detail；Especially absolute predominance is occupied in processing non-stationary signal application aspect wavelet analysis.
But for non-stationary image transmitting in practical application, not enough spirit relatively simple in characteristic processing more differentiating
It is living.In terms of digital signal extraction, which can reflect very well entirely embodies image frequency domain information, but cannot be objective
It extracts local time related with frequency domain signal and both time-domain and frequency domain cannot be integrated intrinsic highlight.
For non-stationary image transmitting in practical application, it is necessary to consider that overall time function is distributed, because signal is in energy function
The slight change of time-domain will all influence signal in entire windowing function spectral change trend.Originally it is mentioned when handling the problem
Windowing Fourier transformation, objective are to overcome the shortcomings of that traditional Fourier, can be by signal to local temporal transformations in short-term out
The middle function of time is sliced into several time intervals, to lock the corresponding frequency in its interval.The letter but this method once opens a window
Number determination, the distribution of frequency domain window is also just fixed, this, which certainly will cause window to stretch or stretch, makes troubles, and has to its image
Resolution characteristics change it is also further difficult, it is necessary to choose windowing independent variable and dependent variable again.
It is therefore proposed that a kind of digital image processing method based on local time-frequency domain conversation is very important.
Summary of the invention
(1) goal of the invention
The present invention provides a kind of digital image processing method based on local time-frequency domain conversation, and this method can the above characteristic
It is that both small echo, filter are combined into consideration, is that the wavelet analysis rapidly extracting of discrete signal creates certain supremacy clause.
(2) technical solution
In order to achieve the above object, a kind of digital image processing method based on local time-frequency domain conversation of the present invention, comprising:
S1, digital picture Time-Frequency Domain Filtering device is obtained using discrete wavelet analysis method；
S2, acquisition denoising digital picture is filtered by Time-Frequency Domain Filtering device to noisy data image signal to be processed
Signal；
S3, using soft or hard wavelet threshold, to treated, data image signal carries out second denoising processing.
The Time-Frequency Domain Filtering device includes low-pass filter h (ω) and high-pass filter g (ω), is met:
|h(ω)|2+|h(ω+2nπ)|2=| g (ω) |2+|g(ω+2nπ)|2=2,
h(ω)g*(ω)+h(ω+2nπ)h*(ω+2n π)=0；
N ∈ Z, Z are the set of whole integer, h*(ω) is the conjugate function of h (ω), g*(ω) is the conjugation letter of g (ω)
Number.
The step S1 includes:
S1a, Hilbert transformation is done to the high-frequency signal part of primary power signal function F (t), enables function space L2(R)
It is the square integrable of Hilbert envelope function, forDefine continuous wavelet transform function；Wherein, R is complete
The set of body real number；
S1b, it is analyzed based on discrete wavelet, discrete transform is carried out to continuous wavelet function, obtains DMT modulation
Function；
S1c, the wavelet transform function progress multiresolution analysis to acquisition, acquisition low-pass filter and high-pass filter
Filtering parameter.
The step S3 includes:
S3a, noisy data image signal to be processed is subjected to gray proces, obtains gray level image；
S3b, selection threshold value, acquisition multiple grades gray level image are passed through to gray level image；
S3c, binary Images Processing and analysis are carried out to gray level image, obtains binaryzation gray level image；
S3d, it after extracting low frequency signal to binaryzation gray level image using soft and hard threshold, is obtained using threshold segmentation method true
Real picture signal.
Extracting low frequency signal to binaryzation gray level image using soft and hard threshold in the step S3d includes:
After the high-frequency signal in the gray level image image of hard -threshold removal binaryzation, low frequency letter is extracted using soft-threshold
Number.
Optionally, before the step S3, it is further comprising the steps of at least one step:
S30a, to treated, picture signal carries out the disposal of gentle filter；
S30b, using small wave converting method, to treated, picture signal carries out compression processing；
S30c, using frequency domain method wavelet transformation, to treated, picture signal carries out image enhancement processing.
The step S3b includes:
S3b1, treated picture signal low frequency signal and high-frequency signal are decomposed, acquisition picture signal piece；
S3b2, multiple resolution scale order are resolved into again after wavelet transformation to picture signal piece；
S3b3, to the minimum constituent unit decorrelation in resolution scale order after, obtain coding-belt transformation coefficient；
S3b4, coding-belt transform coefficient matrix is quantified, obtains compressed bit stream, and added in compressed bit stream for repairing
Multiple code error special identifier symbol；
S3b5, the paragraph header message for being used for ID resolution rank order is stored in the front of the compressed bit stream of generation.
The step S3a includes that treated, picture signal is carried out using mean filter method or median filter method
The disposal of gentle filter.
The step S3c includes, and first to treated, image carries out Fourier transform in frequency domain, after to the frequency spectrum of image
Digital filtering reparation, finally, the image after will be modified carries out inverse fourier transform.
(3) beneficial effect
The beneficial effects of the present invention are: the present invention is using mixing nonlinear smoothing filter in conjunction with single threshold value wavelet filtering
Mode can solve the problems, such as mixed Gaussian and impulsive noise image denoising, this is by resolution analysis, the Minutiae extraction to image
With certain practical significance.
Detailed description of the invention
Fig. 1 is a kind of digital image processing method flow chart based on local time-frequency domain conversation of the embodiment of the present invention；
Fig. 2 is spectrogram after initial function of embodiment of the present invention Hilbert transformation；
Fig. 3 is that Hilbert of the embodiment of the present invention converts envelope promotion effect diagram；
Fig. 4 is that Hilbert of the embodiment of the present invention converts envelope extraction and signal modulation schematic diagram；
Fig. 5 is that Hilbert of the embodiment of the present invention converts any envelope image overall effect schematic diagram；
Fig. 6 is gray proces front and back effect diagram in denoising of the embodiment of the present invention；
Fig. 7 is initial position threshold value and signal relation schematic diagram in denoising of the embodiment of the present invention；
Fig. 8 is final position threshold value and signal relation schematic diagram in denoising of the embodiment of the present invention；
Fig. 9 is signal two-value Contrast on effect schematic diagram before and after the processing in denoising of the embodiment of the present invention；
Figure 10 is Contrast on effect schematic diagram before and after de-noising of the embodiment of the present invention；
Figure 11 is de-noising of embodiment of the present invention front signal and frequency domain relation schematic diagram；
Figure 12 is signal and frequency domain relation schematic diagram after de-noising of the embodiment of the present invention；
Figure 13 is theory of wavelet transformation of embodiment of the present invention figure；
Figure 14 is Contrast on effect schematic diagram before and after wavelet transformation of the embodiment of the present invention；
Figure 15 is the low high-frequency decomposition schematic diagram of wavelet transformation of embodiment of the present invention primary power；
Figure 16 is wavelet transformation of embodiment of the present invention first time compressed dimension and byte relation schematic diagram；
Figure 17 is second of compressed dimension of wavelet transformation of the embodiment of the present invention and byte relation schematic diagram；
Figure 18 is the image effect contrast schematic diagram after noisy image of the embodiment of the present invention and smoothing processing；
Figure 19 is noisy image time-domain and frequency-domain relation schematic diagram before picture smooth treatment of the embodiment of the present invention；
Figure 20 is time-domain and frequency-domain relation schematic diagram after picture smooth treatment of the embodiment of the present invention；
Figure 21 is that the present invention is based on the method flow diagrams of frequency-domain model image enhancement；
Figure 22 be image enhancement of the embodiment of the present invention before with effect contrast schematic diagram after image enhancement；
Figure 23 is low frequency signal distribution schematic diagram before image enhancement of the embodiment of the present invention；
Figure 24 is low frequency signal distribution schematic diagram after image enhancement of the embodiment of the present invention.
Specific embodiment
In order to preferably explain the present invention, in order to understand, below by specific embodiment, present invention work is retouched in detail
It states.
In the filtering of picture signal as, signal primary power function can generally be regarded into a kind of more complicated, disturbance
Variation wave, however the complex wave is formed by several outs of phase, various amplitude and the different sine wave lamination of frequency.It is former
There is the outstanding feature of Fourier algorithm to be closely connect the time of corresponding wave and frequency both sides relation, using more
The clearly demarcated frequency spectrum of waveform, which goes to analyze, obscures node or scattered cake within the scope of corresponding time-frequency；But Fourier algorithm is for the time-frequency that localizes
Specificity analysis is poor.If the signaling point of some time point or segment locating for image, signal patch (ten are expected in its receiving end
Point accurately when signal), at the same time, phenomena such as signal of time-frequency domain generally will appear redundancy or messy code occurs appearance,
And original Foureir algorithm can only carry out processing analysis to whole time-frequency domain signal.Therefore, no matter wavelet analysis is in the time
It is higher, more quasi- that degree is precisely analyzed to the characteristics of image of small area in domain, frequency domain, and adaptivity is stronger；So small wavelength-division
Analysis is not only able to satisfy the pulse train coding and galvanomagnetic-effect of time-frequency domain signal, but also for any time node and can appoint
The various distortion that occur in the case of what frequency, catastrophe characteristics more sensitivity are captured and are acquired.
For wavelet transform filtering can approximation regard a low-pass filter as, compared to for more traditional filtering, especially mixed
Closing can keep fine scale in original signal and texture intrinsic in Gaussian noise；At the same time, wavelet transformation is in local time-frequency
Domain window can be adjusted as signal waveform is different, and linked character signal between adjacent scale can be protected very well
It holds；In other words it can embody local message is intact；Specific manifestation are as follows: (1) stationary signal can take time window to come greatly
Increase frequency domain resolution；(2) non-stationary signal can equally find Perfect Time position with lower frequency region resolution ratio.Therefore, originally
Patent can solve mixed Gaussian and impulsive noise using mixing nonlinear smoothing filter and single threshold value wavelet filtering combination
Image denoising problem, resolution analysis, the Minutiae extraction to image are had certain practical significance by this.Believe for non-stationary
Number, this method uses Digital Image Processing of the wavelet transformation based on local time-frequency domain conversation.
Several concepts of wavelet transformation are given below.
If primary power signal function is f (x), the present embodiment is from primary power signal function f (x) ∈ L2(R) start with, tie
Local time-frequency domain texture characteristics can be highlighted for non-stationary signal image by closing wavelet transformation；DefinitionAndIf wavelet functionFourier transformationMeet:
ThenFor a wavelet function or mother wavelet function, by mother wavelet functionAfter flexible and translation
,
a,b∈R；A ≠ 0, R are real number.
For wavelet function, a is to stretch or compress the factor, and b is shift factor.
By carrying out flexible to signal sequence and translating mathematical modeling analysis；It is mainly characterized by:
(1) stationary signal can take time window to increase frequency domain resolution greatly；(2) non-stationary signal can equally use
Lower frequency region resolution ratio finds Perfect Time position.To further image procossing be pushed to develop in time-frequency domain local shape factor
With certain application value.
For arbitrary function f (x) ∈ L2(R) continuous wavelet transform Wf(a, b) are as follows:
For same signal, its time domain and frequency domain all follow the conservation of energy in any Complete Orthogonal concentration function
Known to this universal law:
For containing noise, dirt high-frequency signal function g (x),
Function f (x) integrable, f (x) ∈ R are made for any x ∈ [- π, π]2(x)；g(x)∈R2(x) it all sets up.Therefore
And numerical value of the corresponding wavelet transform function of morther wavelet in the interval range is also constant；Only the wavelet function is discrete
Variation changes, and can also be expressed as follows:
Illustrate f (x) backstepping formula exist, and it can be seen that its time-frequency domain local signal convert when signal pressure
The loss of signal is almost 0 during contracting, enhancing or even filtering and noise reduction etc.；Wherein R*≠0∪R*∈R；R is the collection of all real numbers
It closes.
The present embodiment provides a kind of digital image processing methods based on local time-frequency domain conversation, as shown in Figure 1, specifically
Ground includes the following steps:
S1, Time-Frequency Domain Filtering device is obtained using discrete wavelet analysis method.
Wherein, the Time-Frequency Domain Filtering device includes low-pass filter h (ω) and high-pass filter g (ω), is met:
|h(ω)|2+|h(ω+2nπ)|2=| g (ω) |2+|g(ω+2nπ)|2=2,
h(ω)g*(ω)+h(ω+2nπ)h*(ω+2n π)=0；
N ∈ Z, Z are the set of whole integer, h*(ω) is the conjugate function of h (ω), g*(ω) is the conjugation letter of g (ω)
Number.
Specifically, this step includes:
S1a, Hilbert transformation is done to the high-frequency signal part of primary power signal function F (t), enables function space L2(R)
It is the square integrable of Hilbert envelope function, forDefine continuous wavelet transform function；Wherein, R is complete
The set of body real number.
Enable L2(R) be Hilbert envelope function square integrable, and haveTherefore:
As shown in Fig. 2, phase and Convolution Properties to show on Fourier transformation narrow-band filtering in Hilbert transformation
It is especially prominent, and be usually used to do a kind of data processing method of Envelope Analysis, it is that sin signal passes through the H in Hilbert first
Become cos signal, then this is obtained into signal Hilbert is transformed to complex signal twice, and negative signal is solved to it；And it to protect
The composite signal frequency spectrum for demonstrate,proving Hilbert transformation is less than Nai Shi frequency spectrum, finally that the complex signal acquired is orthogonal with original signal.Pass through
Hilbert transformation, eliminates noisy dust particles but to save crucial texture intrinsic.
Then there is function F (x), the inner product of G (x) may be expressed as:
G (x) refers to containing noise, dirty high-frequency signal function.
Meanwhile function F (x) ∈ L2(R) Fourier transformation may be set to:
Fourier transformation for function G (x) is
For function F (x), G (x) andIt is all satisfied Parseval identity:
Therefore, in the analysis of centre frequency narrow band signal, first to initial function F (x), the high-frequency signal part of G (x) is done
Hilbert transformation.
Frequency is set as 20Hz in Hilbert Envelope Analysis, and the waveform of envelope signal is that the absolute value of cosine signal is believed
Number, due to taking absolute value when calculating envelope, so that signal frequency be made to double.Envelope is promoted, far from 0, as shown in Figure 3.
Refering to what is shown in Fig. 4, it can be seen that Hilbert Envelope Analysis can effectively extract envelope and frequency modulating signal, and
Detection has the same effect.As shown in figure 5, for the envelope of an arbitrary shape, it can be seen that except in addition to there is error in edge,
Overall effect is fine.
For wavelet transform function: can define its expression formula is f (x) ∈ L2(x),
If corresponding Fourier transformation conditional functionMeet:
ThenFor basic wavelet function.By basic wavelet functionAfter flexible and translation,
For wavelet function, a is to stretch or compress the factor, and b is shift factor.
For arbitrary function f (x) ∈ L2(R) continuous wavelet transform CTf(a, b) are as follows:
A ≠ 0, b, x be can continuous variation coefficient,Between be conjugated；With Fourier transform
Known to: coefficient of dilatation a,
Therefore, a is smaller,Frequency spectrum function is toward close, time-domain function at wave crestWaveform constantly compresses；Instead
It, a is bigger,Waveform extends, frequency spectrum functionIt is approached toward trough；So functionIn x ≈ 0, waveform
Significant change can be just showed, successively decreasing further away from origin waveform, it is further significant to change.At the same time, for arbitrary parameter (a, b), base
Plinth wavelet function can occur significantly being slightly variable at the position x=b again, and certainly as time-frequency domain increases, function constantly successively decreases directly
Extremely
Continuous wavelet transform CTf(a's, b) is inversely transformed into:
Wherein, f (t) is the continuous wavelet function after inverse transformation, CTfFor morther wavelet transformation
Continuous wavelet function has the property that
Initial signal energy function is f (x), if the wavelet transformation of f (x) is FTa,b。
Locality: initial signal energy function is f (x), can take respective function numerical value on the periphery x=0, wherein f (x)
=0 is unable to value；So can be using real number or complex function as the morther wavelet of wavelet function, when may make just now in time-frequency domain
Frequency domain has locality.
Decomposability: can convert mother wavelet function and be equal to the factors of two decomposition and form, and sum be superimposed, then this
When, f (x)=f (x1)+f(x2)；One function decomposition can be two function representations by then continuous wavelet are as follows:
TIME SHIFT INVARIANCE: if the wavelet transformation of f (x) is FTa,b；Then the wavelet transformation of f (x-t) is FTa,b-t；Both sides relation
It may be expressed as:
Fluctuation: it knowsWavelet function exists in fluctuation alternating nature, the fluctuation of wave function alternately KTf
(a, b) are as follows:
In practical applications, there is also larger redundancies for continuous wavelet functional transformation, therefore, KTfThe mould pole of (a, b) function
Big value can be used the reconstruct of MALLAT iteration signal and indicate.
S1b, it is analyzed based on discrete wavelet, discrete transform is carried out to continuous wavelet function, obtains DMT modulation
Function；
During practical communication, signal is generally with discrete signal formal distribution；So to continuous wavelet must to its from
Dispersion transformation, if by continuous wavelet it is discrete it is necessary to meet following condition for small echo, this section is discussed in detail with regard to the problem emphatically
And elaboration.
For dyadic wavelet, it will be appreciated that it is half wavelet transform, i.e., discrete transform is used to scale coefficient, so that
Shift factor continuous transformation.
For continuous wavelet function:
A=2j, j ∈ Z,
A is graphical rule exponential function, and Z is integer or focusing multiple
Then dyadic wavelet function are as follows:
For f (x)=L2(R) corresponding dyadic wavelet transform function is
Wherein, j is scale factor,For discrete transfer function.The focusing multiple of scale factor j and image is inversely proportional, i.e. j
It is smaller that image local signal can be observed more in every possible way；If can then increase j on the contrary, image overall signal is distributed
Numerical values recited；Therefore, numerical value j is for particularly significant in picture signal analysis in dyadic wavelet.
Fourier transform functionIt needs to meet:
For
Wherein, G1, G2Finger is received containing noise, dirt minimum, greatest exponential value.
It is to ensure that wavelet function becomes the adequate condition of dyadic wavelet.
For discretization wavelet conversion coefficient
If
Then,
At this timeReconstruction formula may be expressed as:
Wherein,It isReconstruction of function then has
It should be noted that in above-mentioned formula,It is stationary value, corresponding Fourier transform functionThen have
May be non-constant, whenWhen for dyadic wavelet,Neither dyadic wavelet, it is also possible to not be small echo.
S1c, the wavelet transform function to acquisitionMultiresolution analysis is carried out, is obtained low-pass filter h (ω) and high
The filtering parameter of bandpass filter g (ω).
Multiresolution analysis refers to integral status, the general name of process development essence for disclosing a things；When target source with examine
When feeling that spacing is larger between the visual field, it is capable of whole scapes of rather objective, the present fairly a certain image within sweep of the eye
It sees, outstanding feature shows as that region inside dimension is larger, information content is full, image is more fuzzy, region dot matrix is lax, can only will
The general panorama of lock onto target, it is not careful enough to hold with regard to the scrappy information of detail；Conversely, then image-region target zone compared with
It is small, scale is subtleer, the pixel of picture is higher, dot matrix is further intensive, can embody in every possible way image substantive characteristics and
It Individual features but is not easy to hold image overall feature.
To image global feature and local detail hold very well, then the distance of the similarities and differences can be used to goal object
It examines, in this process due to selection criteria difference, so that image detail, motion feature also will appear different variations
And result；Therefore part and whole dynamic change between the two can be observed using difference numerical method.But it is only worth noting
, because things is different in the Characteristics of Development in each stage, reflected scale is different, so with different numerical value
Method is also critically important, particularly significant using applicable qualitative numerical method to its specific things.
According to the approximation characteristic property of multi-resolution characteristics, have to so that primary power signal function f (x) ∈ L2(R)
It is closed subspace VjMeet claimed below:
Monotonicity:
It is fully progressive:
Retractility:
Translation invariant:
Riesz base: function f (x) ∈ V if it exists0Can constitute { f (x-i), i ∈ Z } Riesz base, then for about
Unique arrangement set a of Riesz basic sequence setkHave:
Its VjThe orthonormal vectors group in space may be expressed as:
V simultaneouslyjOrthonormal vectors group beSo can have a Double-scaling equation:
Wherein, { h (i), i ∈ Z } ∈ L2, arranged for scale coefficient.
Define VjIn Vj-1The orthocomplement, orthogonal complement in space is Wj,j∈Z,
It is denoted as:
Then orthocomplement, orthogonal complement is closed sequence of subspaces { Wj, j ∈ Z } it is straight and be L2(R):
Wavelet functionScaling functionAre as follows:
If takingThen
For wavelet transform functionAre as follows:
Then f (x) resolution ratio be j complete asymptotic discrete function with can f (x) in VjMark projection between relationship can indicate
Are as follows:
F (x) is in local feature, that is, f (x) that resolution ratio is j in WjThe orthogonal complement space projection are as follows:
Wherein,Respectively f (x) is in Vj、WjProjection.
It enables:
The then wavelet transform of finite energy signal function f (x) are as follows:
According to wavelet functionAnd scaling functionThe two characteristic can indicate with two-scale equation, Vj、WjPoint
Not corresponding inner product diagonal matrix (orthogonal normalizing base) is
Because in scaling function Double-scaling equation:
Use Vj, the basic function of j=-1Item in series expansion Double-scaling equation enables h for exhibition
The factor is opened, then scaling function indicates are as follows:
Secondly, for wavelet function Double-scaling equation: V-1-V0=W0, wherein W0For double scale coefficients.It is found thatIn other wordsV can be usedj, the orthogonal basis of j=-1Expansion
Series, enabling g is unrolling times, then scaling function indicates are as follows:
Formula one, formula two are all the multiresolution analysis expression formula of scaling function, wavelet function；Be unfolded in its equation because
Sub- h, g are unrelated with j；And have j it is adjacent with any two in
It is related；So filtering parameter h (ω), g (ω) are as follows:
Continuous signalFourier transformation；
H (ω), g (ω) are discrete signal h (x), are converted in Fu of g (x).
Therefore, h (ω), g (ω) are the parameter of filtering group, and filtering group coefficient has following property:
The filter factor summation of two kinds of functions is definite value:
The summation of frequency domain initial value is definite value:
Wherein, h (ω) |ω=0、g(ω)|ω=0Respectively low, high-pass filtering parameter.
Recursion property:
Low pass, high-pass filter particular requirement:
|h(ω)|2+|h(ω+2nπ)|2=| g (ω) |2+|g(ω+2nπ)|2=2
h(ω)g*(ω)+h(ω+2nπ)h*(ω+2n π)=0
S2, noisy data image signal to be processed is filtered by low-pass filter and high-pass filter
It makes an uproar data image signal.
The above characteristic is that both small echo, filter are combined consideration, this is quickly mentioned for the wavelet analysis of discrete signal
It takes and creates certain supremacy clause.
It, can be by by noisy digital picture to be processed based on low-pass filter and high-pass filter that step S1 is obtained
Signal is filtered acquisition denoising data image signal by low-pass filter and high-pass filter.
S3, using soft or hard wavelet threshold, to treated, data image signal carries out second denoising processing.
Ground frequency domain is distributed in signal function and the signal area containing impurity noise is significantly different, usually in high-frequency region
There are certain granules suspension, image spike, texture and edge features；Useful signal distribution is present in low frequency region, to its figure
Need to carry out proper treatment with noise intersection area to signal when as filtering just now will not lose image important feature, the region model
Farmland also small scale excessive can not can not also extend very much；So how can preferably keep image certain specific in image procossing
Minutia also can de-noising to the full extent become image denoising head in it is weight.
Wherein, the smaller factor is rejected in the method and is set to 0, usually because reservation wavelet coefficient is larger in hard -threshold
It will appear biggish variance, so that key node position can be made to occur fluctuating by a relatively large margin.And it can make in suitable threshold
Outcome function is discontinuous at value γ, cannot obtain and the consistent signal sampling of initial pictures.For the soft-threshold that compares, return direct
Lesser wavelet parameter is deleted, the larger wavelet coefficient remained is done into retraction processing.It also results in and is greater than in this process
There is large error in retraction in the wavelet coefficient of threshold gamma, and the signal after generally making denoising becomes further smooth, still
Also certain features in picture signal can be made more or less to lose.Therefore, usually when using wavelet threshold processing image problem,
Improvement promotion can be carried out using soft and hard threshold combination method.
If initial pictures are { f [x, y]: x, y=1,2......N }, Noise pollution image is
{ g [x, y]: x, y=1,2......N }
Meanwhile enabling noise jamming value is { ε [x, y]: x, y=1,2......N }, then has:
{ g [x, y]=f [x, y]+ε [x, y]: x, y=1,2......N }
Wherein, { ε [x, y]: x, y=1,2......N } and { f [x, y]: x, y=1,2......N } independently of each other, is denoised
Final purpose be can to obtain from { g [x, y]: x, y=1,2......N } initial pictures f [x, y]: x, y=1,
2......N } data are aboutError amount between the two is η, then has:
After orthogonal transformation, it can obtain:
Y [x, y]=X [x, y]+V [x, y]: x, y=1,2......N
Y [x, y] is the Noise small echo factor, and X [x, y] is the noiseless small echo factor, and V [x, y] is noise component(s), and is distributed
In N (0, σ2 n) on.It can obtain the small echo factor of signal from the Noise small echo factor Y [x, y], noise wavelet is eliminated with this
The factor.
Specifically, this step includes:
S3a, noisy data image signal to be processed is subjected to gray proces, obtains gray level image；
Signal energy concentrates in lower frequency region, i.e., small echo factor value is larger at this time；And noise concentrates in high-frequency domain, this
It is less than normal to carve wavelet coefficient amplitude.Firstly, original image is passed through gray proces, i.e., in RGB model, if Red=Green=
When Blue, a kind of particular color can be indicated with colour at this time, the value of R=G=B is referred to as gray value at this time, so, at gray scale
The each dot matrix of image after reason can only store a Bit gray value, and gray scale codomain is 0-255.The ash at coordinate (i, j) can be enabled
Degree image is f1 (i, j)=R (i, j) f2 (i, j)=G (i, j) f3 (i, j)=B (i, j)；Wherein, R component grayscale image；G component
Grayscale image；B component grayscale image.As shown in fig. 6,
Have { g [x, y]=f [x, y]+ε [x, y]: x, y=1,2......N } initial pictures be f [x, y]: x, y=1,
}, 2......N Noise pollution image is { g [x, y]: x, y=1,2......N }；Enabling noise jamming value is { ε [x, y]: x, y
=1,2......N }；As threshold value constantly increases, signal function variation is further significant, and as shown in Figure 7, Figure 8, small echo is become
It changes for method, wavelet coefficient is bigger than normal to show as signal energy, and the small echo factor is less than normal to show as noise, therefore can pass through threshold value
Method retains the larger coefficient of amplitude, while removing wavelet coefficient amplitude less than normal.
S3b, selection threshold value, acquisition multiple grades gray level image are passed through to gray level image；
Original image is made to highlight black and white lattice original rgb color pixel the good image of above-mentioned gray proces, and
Gray value can be set as to 0/255, multiple grades gray level image is then obtained with this by selection appropriate threshold again.
S3c, binary Images Processing and analysis are carried out to gray level image, obtains binaryzation gray level image.
Obtaining result still can embody image entirety and local feature binary picture.Because for Digital Image Noise
It generally all needs to carry out binary Images Processing and analysis to it, by the good image binaryzation of gray scale；It may make related with image property
0/255 corresponding lattice position save.As shown in figure 9, other are with pixel, related multilevel values are rejected substantially, so that at image
Reason becomes simpler, and it is high to shorten picture signal process, compression efficiency.
S3d, it after extracting low frequency signal to binaryzation gray level image using soft and hard threshold, is obtained using threshold segmentation method true
Real picture signal.
Ideal binary digital image is generally obtained, commonly uses shielding, threshold value bound is irised wipe in the limit of crosslinking
Codomain.I.e. certain wavelet coefficient >=given thresholds may be defined as certain objects (gray value 255), remaining is except the region
Pixel (gray value 0)；Also it can be regarded as image background, if there are consistent inhomogeneous intensity values with regard to a certain image essence, and be in
One with gray scale be 0 homogeneous background under the conditions of, soft and hard threshold can be used extract low frequency signal, make useful signal with it is miscellaneous
Matter segmentation, then available signal is filtered out using threshold segmentation method, realize that gray scale difference is converted with this.
Secondary denoising is carried out to its figure map by MATLAB, obtain as in Figure 10, Figure 11 and Figure 12 about signal
It is known with frequency domain relationship: being still Gaussian distribution after wavelet transform process p (m, n)=P, in other words Gauss white noise
Sound is uniformly scattered in dimensions in frequency whole space；And transformed signal is scattered in dimensions in frequency local space, in energy
Limited angle sets out: the noise of i.e. contaminated image is concentrated in whole small echo factors, and signal energy concentrate on part small echo because
On son.For this purpose, the small echo factor can substantially be divided into two kinds: (1) being generated after the transformation of contaminated noise wavelet, quantity is small, wave at this time
Half of the peak to trough distance (i.e. amplitude is big)；(2) the transformed amplitude of signal is small, and quantity is more.Therefore it can be according to magnitude parameters
Difference, to remove picture noise part, at the same time, saves image local minutia a critical value is arranged very well.
Since current cloud computing, big data era are born, the multimedia technologies such as image procossing and machine vision also day therewith
The different development of crescent, it is also higher and higher to the code stream requirement of image transmitting, suspension generally need to passed through using Noise Elimination from Wavelet Transform
The different steps such as grain denoising, compression of images, smoothing processing, signal enhancing, image co-registration.
Optionally, before step S3, it is further comprising the steps of at least one step:
S30a, to treated, picture signal carries out the disposal of gentle filter；
In the step S30a, the method for the disposal of gentle filter includes the method for mean filter and median filtering.
Mean filter-Gaussian noise
Mean filter is also known as neighborhood averaging, is a kind of about local space filtering processing algorithm.Its purpose is that with a certain
The average gray of all pixels substitutes the initial gray value of the pixel in a pixel neighborhood of a point.This method numerical operation letter
Easily but there are significant drawback, it is presented as that image image pixel into after crossing mean filter processing is decreased obviously, main reason is that
In average value alternative Process, it changes the gray value of original whole domain pixel, and the signal especially in low frequency region, this will make
It obtains original signal to be distorted or be distorted, so that treated, image is in ambiguous morphology.In addition to this, smooth low frequency filtering
Method also plays the role of elimination (as shown in figure 18) to picture noise, by seeking the mean value of neighbouring pixel point, to determine image
The bigger noise smoothing degree of fuzziness, i.e. neighborhood value is better, image is more clear；But once neighborhood value is excessive, this will will lead to figure
Picture edge feature loss is further obvious, eventually image is thickened；Not only operand is very big for the method, and selects
Suitable neighborhood value is also difficult, therefore does not usually consider low pass smothing filtering algorithm.
Its concrete principle are as follows:
If f (x, y) is the image of a width dot matrix N × N, (x, y) refers to some pixel in the selection area, and S is (x, y)
The set of neighbouring central space domain pixel, M are pixel total number, and f (x, y) → g (x, y) is mean filter treated figure
Picture, then
In formula (x, y)=0,1,2,3...........N-1；Radius in the region S is R, and R value is bigger, and fuzziness is bigger；
I.e. neighborhood territory pixel point set average gray value substitutes original noise pollution pixel, although eliminating noise to a certain extent in this way
Pollution, but the pixel coordinate value containing noise pollution also changed originally, this will will lead to the change of soft edge degree
Greatly.
Median filtering-impulsive noise
Median filtering is one of nonlinear filter common method, and processing method is similar and right with neighborhood averaging
The neighborhood territory pixel coordinate set of some pixel operates it, and it is to take being averaged for neighborhood territory pixel point summation that difference, which is it not,
Value, but substituted with the intermediate value of the neighborhood each point pixel.
The specific steps are that:
The first step, in image N × N array, certain point (x, y) central pixel point, chooses one suitably just if it exists
Square Neighborhood pixel coordinate set S.
Second step is successively ranked up the pixel gray value in square neighborhood territory pixel coordinate set S according to size,
Choose the output valve of pixel (x, y) centered on the median of the sequence group.
Value principle during screening sequence gray scale median:
If gathering pixel total number M=2n+1, n ∈ N in the neighborhood+, then remember that the gray value of sequence intermediary image vegetarian refreshments is
Output valve.
If gathering pixel total number M=2n, n ∈ N in the neighborhood+, then remember the average ash of two pixels among sequence
Angle value is output valve.
To sum up, median filtering expression formula can be concluded are as follows:
Y (n)=medM=med [x (n-N) ... ... .x (n) ... .x (n+N)]
In formula, M=[x (n-N) ... ... .x (n) ... .x (n+N)] is center pixel Neighbourhood set pixel,
Med [] is indicated the arrangement set whole numerical value by taking intermediate grey values after monotonic increase or descending order.
Through comparing front and back character image using median filtering known to the image polluted by Figure 18 containing Gaussian noise；In it was found that
Value filtering can preferably effectively remove Gaussian noise, and the picture noise after smoothing processing is preferably inhibited, main former
The region or section are approximately equal to because being that the intermediate value after sequence can change the pixel value near low frequency useful signal
Pixel-matrix it is identical, with this have the function that remove noise.And in Figure 19: the x1=10 in the coordinate of same time domain,
Y1=50 and x2=18, y2=55；But in Figure 20 time-frequency domain figure, x1=10, y1=35 and x2=18, y2=30；Numerical value is bright
It is aobvious to reduce, it mainly shows noise disturbance and is remarkably decreased, either in corresponding peak position or any other positions time-frequency domain
Coordinate values all decrease；And the corresponding grid that influences of image after smoothing processing is further bright and clear compared with Figure 19, can not show a candle to initially flat
Intensive disturbance before sliding, shows as that signal distributions are more uniform, redundancy impurity suspended particulate is all low pass filtering, therefore makes an uproar this moment
Sound can be inhibited in a certain range, and can protect the important informations such as image spike, texture and image detail feature, profile
It stays intactly, it is more obvious, clear to reach image ambient signal.
S30b, using small wave converting method, to treated, picture signal carries out compression processing；
Because digital picture is made of a large amount of collective datas, general pattern can all have information redundancy, associated with each other relatively strong
Etc. factors exist, so Effective selection go out low frequency (useful signal), eliminate redundancy (time redundancy, three-dimensional space redundancy, letter
Number with knowledge redundancy, character redundancy) can both play compression to data, image attribute itself will not be damaged.Its image pressure
Contracting purpose is to indicate image itself with the smallest Bit, cannot damage compressed image pixel and quality in the process.It passes
The DCT compression method of system is that data feature related with symbol in image is indicated using coordinate vector based on orthogonal transformation method；One
Will result in DCT when denier message capacity is larger, image complexity is bigger than normal can only handle basic voice and knowledge module；So new
Type wavelet transformation compression energy effectively reduces on the basis of discrete transform or even eliminates " interference of mosquito formula ", " cellular noise ", " sheet
Noise " and " incident noise "；Image sheet amount, naked eyes visual effect are differentiated using local temporal and frequency domain method
Rate and signal band correlative coding coincide, and can collect the biggish coefficient subband of the small echo factor, this all can be directly to image
Compression strap carrys out positive effect.
It can be divided into according to picture quality quality evaluation method is measured known to de-noising evaluation method: subjective consciousness evaluation and objective
Theorem is judged.The former is to establish ground on the basis of (MSE) and (PSNR) to judge criterion, be may be defined as:
N in formulaxNyThe dot matrix of image in the horizontal direction and the vertical direction is respectively indicated, f (i, j) indicates the ash of the image
Functional value is spent, F (i-j) indicates gray value of the image after processing.
Therefore, the objective evaluation compare subjective consciousness judgement more effectively the pixel of image and quality can be made it is objective
Judge, reason be this method can by image by least mean-square error reflection compress before and after image overall situation and area
Not, but dot matrix all for image is objectively evaluated and are all lumped together, mobility is poor.
Wavelet transformation can mainly provide reliable image localised information, and minutia any for image can be using essence
Thin time-domain and frequency-domain node calculates, without damaging the original feature of picture signal；Its detailed process is shown in Figure 13, i.e., is mother by signal decomposition
Small echo obtains a series of wavelet sequences carrying out Pan and Zoom, and formula is as follows:
Wherein, scale, position are respectively zoom factor, translation location parameter, and wavelet transform signal f (t) is used
Scaling, shift factor replace the result after fourier function sine and cosine wave conversion；Only in discrete calculation, in comparison
Scale, position coefficients comparison are small.
The S30b, using small wave converting method, to treated, picture signal carries out compression processing；Include:
S30b1, by treated, picture signal is decomposed, and obtains picture signal piece.
Initial pictures are subjected to component decomposition；It is usually needed simultaneously firstly, consider the size of image, if image is larger,
Component map after decomposition need to be divided into several signal patch, if image is smaller as, entire picture can be regarded to a signal patch.Initially
The minimum basic unit that image and component decompose image is signal patch." rectangular bulk " can be prevented by drawing the multiple segment signal pieces of part in this way
The generation of effect.
S30b2, multiple resolution scale order are resolved into again after wavelet transformation to picture signal piece；
Signal patch resolves into multiple resolution scale order again after wavelet transformation.
S30b3, to the minimum constituent unit decorrelation in resolution scale order after, obtain coding-belt transformation coefficient.
Resolution scale order minimum constituent unit is signal band decorrelation coding-belt.It is worth noting that after decorrelation
Coding-belt transformation coefficient can embody differentiate rank, the frequency domain feature of piece component.
S30b4, coding-belt transform coefficient matrix is quantified, obtains compressed bit stream, and add and be used in compressed bit stream
Repair code error special identifier symbol.
To the coefficient carry out " encoding block " matrix quantization, in the process the bit plane in encoding block by key order from
It is main to obtain compressed bit stream to time closely related coding of progress coefficient information metric, for convenience to code error reparation, so in code stream
Middle addition special identifier symbol.
S30b5, the paragraph header message for being used for ID resolution rank order is stored in the front of the compressed bit stream of generation.
There are a paragraph header message in front of the code stream of generation, for explaining the decomposition levels order of initial pictures；Decoding end
It, in conjunction with own actual situation, without solving all code streams, can be recreated about initial according to head information above
Image of the image under some specified resolution, in a certain specific region.
S30c, using frequency domain method wavelet transformation, to treated, picture signal carries out image enhancement processing.
After threshold value setting, the small echo factor bigger than normal may be selected to match suitable two scale, multiresolution features image；Herein
2-d wavelet denoising can be used quarter reach targetedly rejecting noisy part and highlights useful signal image-region.Generally according to ruler
It is different to spend feature, wavelet transform components characteristic can be divided into low frequency vector, lateral high frequency, longitudinal high frequency, diagonal high frequency.In conjunction with figure
As actual vector feature, the size of wavelet coefficient is adjusted by changing space structure, energy signal carrying and vector orientation,
It is exactly the amplified signal energy function often said, reduces noise component(s).Therefore, this method can change the wavelet coefficient of high-frequency vector,
Until adjusting until optimal parameter, as image pixel is clear at this time, the apparent characteristics of image of profile.
Common wavelet image Enhancement Method has spatial domain method and frequency domain method, and wherein the former is the pixel click-through with regard to image
What row discussed, it may be assumed that
G (x, y)=h (x, y) * f (x, y)
F (x, y) is initial pictures function, and h (x, y) is space transfer function, g (x, y) represents that treated function.
As shown in figure 21, Fourier transform first is carried out to treated image in frequency domain, after to the frequency spectrum digital of image
Filtering is repaired, finally, the image after will be modified carries out inverse fourier transform.
Frequency domain method wavelet transformation enhances principle: first Fourier transform will be carried out to image in frequency domain, then to the frequency of image
Compose digital filtering reparation, finally, image after will be modified carries out inverse fourier transform so that interesting image feature obtain into
One step enhances as shown in Figure 22, Figure 23, Figure 23.
It should be clear that the invention is not limited to specific configuration described above and shown in figure and processing.
For brevity, it is omitted here the detailed description to known method.In the above-described embodiments, several tools have been described and illustrated
The step of body, is as example.But method process of the invention is not limited to described and illustrated specific steps, this field
Technical staff can be variously modified, modification and addition after understanding spirit of the invention, or suitable between changing the step
Sequence.
Finally, it should be noted that above-described embodiments are merely to illustrate the technical scheme, rather than to it
Limitation；Although the present invention is described in detail referring to the foregoing embodiments, those skilled in the art should understand that:
It can still modify to technical solution documented by previous embodiment, or to part of or all technical features into
Row equivalent replacement；And these modifications or substitutions, it does not separate the essence of the corresponding technical solution various embodiments of the present invention technical side
The range of case.
Claims (9)
1. a kind of digital image processing method based on local time-frequency domain conversation, which is characterized in that the described method includes:
S1, digital picture Time-Frequency Domain Filtering device is obtained using discrete wavelet analysis method；
S2, acquisition denoising digital picture letter is filtered by Time-Frequency Domain Filtering device to noisy data image signal to be processed
Number；
S3, using soft or hard wavelet threshold, to treated, data image signal carries out second denoising processing.
2. digital image processing method according to claim 1, which is characterized in that
The Time-Frequency Domain Filtering device includes that low-pass filter h (ω) and high-pass filter g (ω) meets:
|h(ω)|2+|h(ω+2nπ)|2=| g (ω) |2+|g(ω+2nπ)|2=2,
h(ω)g*(ω)+h(ω+2nπ)h*(ω+2n π)=0；
N ∈ Z, Z are the set of whole integer, h*(ω) is the conjugate function of h (ω), g*(ω) is the conjugate function of g (ω).
3. digital image processing method according to claim 2, which is characterized in that the step S1 includes:
S1a, Hilbert transformation is done to the high-frequency signal part of primary power signal function F (t), enables function space L2(R) it is
The square integrable of Hilbert envelope function, forDefine continuous wavelet transform function；Wherein, R is entirety
The set of real number；
S1b, it is analyzed based on discrete wavelet, discrete transform is carried out to continuous wavelet function, obtains DMT modulation function；
S1c, the wavelet transform function to acquisitionMultiresolution analysis is carried out, low-pass filter h (ω) and high-pass filtering are obtained
The filtering parameter of device g (ω).
4. digital image processing method according to claim 1, which is characterized in that the step S3 includes:
S3a, noisy data image signal to be processed is subjected to gray proces, obtains gray level image；
S3b, selection threshold value, acquisition multiple grades gray level image are passed through to gray level image；
S3c, binary Images Processing and analysis are carried out to gray level image, obtains binaryzation gray level image；
S3d, after extracting low frequency signal to binaryzation gray level image using soft and hard threshold, true figure is obtained using threshold segmentation method
As signal.
5. digital image processing method according to claim 4, which is characterized in that use soft or hard threshold in the step S3d
Value extracts low frequency signal to binaryzation gray level image
After the high-frequency signal in the gray level image image of hard -threshold removal binaryzation, low frequency signal is extracted using soft-threshold.
6. digital image processing method according to claim 1, which is characterized in that before the step S3, further include
At least one step in following steps:
S30a, to treated, picture signal carries out the disposal of gentle filter；
S30b, using small wave converting method, to treated, picture signal carries out compression processing；
S30c, using frequency domain method wavelet transformation, to treated, picture signal carries out image enhancement processing.
7. digital image processing method according to claim 5, which is characterized in that the step S3b includes:
S3b1, treated picture signal low frequency signal and high-frequency signal are decomposed, acquisition picture signal piece；
S3b2, multiple resolution scale order are resolved into again after wavelet transformation to picture signal piece；
S3b3, to the minimum constituent unit decorrelation in resolution scale order after, obtain coding-belt transformation coefficient；
S3b4, coding-belt transform coefficient matrix is quantified, obtains compressed bit stream, and addition is compiled for repairing in compressed bit stream
The wrong special identifier symbol of code；
S3b5, the paragraph header message for being used for ID resolution rank order is stored in the front of the compressed bit stream of generation.
8. digital image processing method according to claim 5, which is characterized in that the step S3a includes, using mean value
Picture signal carries out the disposal of gentle filter to treated for filtering method or median filter method.
9. digital image processing method according to claim 5, which is characterized in that the step S3c includes,
Fourier transform first is carried out to treated image in frequency domain, after the frequency spectrum digital of image filtered repair, finally, will
Image after modified carries out inverse fourier transform.
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