CN106157237A - A kind of based on Fourier Transform of Fractional Order with the image processing method of sub-band division - Google Patents
A kind of based on Fourier Transform of Fractional Order with the image processing method of sub-band division Download PDFInfo
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- CN106157237A CN106157237A CN201510235122.3A CN201510235122A CN106157237A CN 106157237 A CN106157237 A CN 106157237A CN 201510235122 A CN201510235122 A CN 201510235122A CN 106157237 A CN106157237 A CN 106157237A
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Abstract
The present invention relates to technical field of image processing, particularly relate to a kind of based on Fourier Transform of Fractional Order with the image processing method of sub-band division, this method propose a seed belt Fourier Transform of Fractional Order, and expand to two-dimensional sub-band Fourier Transform of Fractional Order.Propose by the image sequence of input is carried out sub-band division, the distribution character concentrated at transform domain energy according to input picture, the subband comprising energy bigger is done fraction Fourier conversion, ignores the subband that energy is less, thus obtain the subband fraction Fourier conversion of a kind of approximation.This invention has been mitigated or eliminated the dependency in image between different frequency, reduces the redundancy of data, and avoids each intersubband cross interference and noise diffusion.Finally, this invention gives the application in terms of image reconstruction and compression of images of the subband Fourier Transform of Fractional Order, test result indicate that the effectiveness of subband Fourier Transform of Fractional Order.
Description
Technical field
The present invention relates to technical field of image processing, particularly relate toA kind of based on Fourier Transform of Fractional Order and sub-band divisionImageProcessing method。
Background technology
In order to implemented effectively and speedily image be processed, usually need original spatial domain picture is transformed into other space with some form, and utilizing the ins and outs in these spaces to carry out certain processing easily, last reconvert makes the return trip empty territory to obtain required effectAsImage filtering, restores, and compresses and enhancing etc..Fourier Transform of Fractional Order is a kind of separable and orthogonal conversion, is widely used the Fourier Transform of Fractional Order of image by image method from image spatial transform to frequency domain.
Fourier Transform of Fractional Order is the Fourier transformation of a kind of generalized form, has the double characteristic of signal time domain and frequency domain.Fourier Transform of Fractional Order is used in Digital Image Processing the reluctant problem of conventional Fourier that is capable of, or makes up the deficiency that conventional Fourier transform is analyzed,AsImage filtering, recovery and expression recognition aspect have preferably application.
In image procossing, the collection most of natural images without obvious granularity noise being broken down into a series of band limit component is collectively referred to as subband.It is that the benefit carrying out processing after subband has by picture breakdown: the image energy in different sub-band is different with statistical property, only the part subband bigger containing energy can be converted, reduce the complexity of algorithm；By frequency decomposition, reduce or eliminate the dependency between different frequency, advantageously reduce the redundancy of view data；After being subband by picture breakdown, all operations can be carried out in each subband respectively, it is to avoid cross interference and noise diffusion.
Summary of the invention
It is an object of the invention to provideA kind of based on Fourier Transform of Fractional Order and sub-band divisionImageProcessing method
The technical solution adopted in the present invention:A kind of based on Fourier Transform of Fractional Order and sub-band divisionImageProcessing method, it is characterised in that: use the subband fraction Fourier conversion of one-dimensional approximation that image is processed, comprise the following steps:
Step 1, by a length ofThe sequence of (even number), being decomposed into length is'sWithTwo sequences,,,Can be obtained fom the above equation,；
Step 2, settingIt isApproximate part, be equivalent toBy a low pass filter；It isDetail section, be equivalent toBy a high pass filter；The frequency respectively allowed in half frequency band due to two wave filter is passed through, so just decomposing a sequence into the set of two band limit components；
Step 3, continuation are decomposed, and image is progressively decomposed into the set of multiple band limit component；It is respectively2 times-down-sampled signal after low pass and high pass filter,WithIt is respectively、'sPoint DFT；
Step 4, general,It is updated to
Can obtainPoint sequence?Discrete fractional Brownian random field during rank；
Step 5, useWithAssociation list is shown asIt is one-dimensional subband Fractional Fourier Transform formula,WithIt is referred to as correlation factor；
If step 6 signalEnergy be concentrated mainly on frequency bandIn addition, XaK () can be approximated to beHere,It isApproximate expression, i.e. approximation subband Fourier Transform of Fractional Order.
2、A kind of based on Fourier Transform of Fractional Order and sub-band divisionImageProcessing method, it is characterised in that: two dimension approximation subband Fourier Transform of Fractional Order can also be used, comprise the following steps:
Step 1, use two dimension chirp signal are to image sequenceIt is modulated, obtains new image sequence；WillBeing divided into four submatrixs, each submatrix hasLength scale
Here,、、、It isRespectively by sequence after Methods of Subband Filter Banks；
Step 2, above-mentioned equation group are write as matrix form and are:
；
It isThe vector space of four sub-sequences composition,It is four filter vector spaces,Be absolute value be all the real number vector space of 1；
,,
Step 3, by simple matrix operations, can obtainMatrix, byMatrix and two-dimensional discrete Fractional Fourier Transform formula
Wherein
Can obtainDuring rankTwo-dimensional sub-band Fourier Transform of Fractional Order
Wherein,,,,It is respectively,,,Two-dimentional Fourier Transform of Fractional Order；
Transformation results is divided into by step 4, subband Fourier Transform of Fractional Order in fractional order territory: low-low frequency, low-high frequency, height-low frequency and four subbands of height-high frequency, when we are rightDo two dimension Fourier Transform of Fractional Order time, i.e.Fractional order territory be divided into four subbands, asEnergy is concentrated mainly on low frequency regionTime, can obtainDuring rankApproximation two-dimensional sub-band Fourier Transform of Fractional Order
。
Beneficial effects of the present invention: the inventive method combines Fourier Transform of Fractional Order and image is processed by filial generation decomposition, image energy in different sub-band is different with statistical property, only the part subband bigger containing energy can be converted, reduce the complexity of algorithm；By frequency decomposition, reduce or eliminate the dependency between different frequency, advantageously reduce the redundancy of view data；After being subband by picture breakdown, all operations can be carried out in each subband respectively, it is to avoid cross interference and noise diffusion.
Accompanying drawing explanation
Figure 1It it is Lena original image.
Figure 2Be exponent number be FrFT during 0.4,0.6.
Figure 3It it is image after reconstruction.
Figure 4Be exponent number be Half-band SB-DFrFT during 0.3,0.6.
Figure 5It is to rebuild image.
Figure 6It is that Quarter-band SB-DFrFT rebuilds image.
Figure 7It is with PSNR during FrFT algorithm 0-1 exponent number.
Figure 8It is with CR during FrFT algorithm 0-1 exponent number.
Figure 9It is to useSB-DFrFT algorithm 0-1 exponent number time PSNR.
Figure 10It is to useSB-DFrFT algorithm 0-1 exponent number time CR.
Detailed description of the invention
A kind of based on Fourier Transform of Fractional Order and sub-band divisionImageProcessing methodUse one-dimensional approximation subband Fourier Transform of Fractional Order or two dimension approximation subband Fourier Transform of Fractional Order zygote generation to decompose image is processed, processing image when using one-dimensional approximation subband Fourier Transform of Fractional Order and filial generation to decompose, it comprises the following steps: step 1, by a length ofThe sequence of (even number), being decomposed into length is'sWithTwo sequences,,,Can be obtained fom the above equation,；
Step 2, settingIt isApproximate part, be equivalent toBy a low pass filter；It isDetail section, be equivalent toBy a high pass filter；The frequency respectively allowed in half frequency band due to two wave filter is passed through, so just decomposing a sequence into the set of two band limit components；
Step 3, continuation are decomposed, and image is progressively decomposed into the set of multiple band limit component；It is respectively2 times-down-sampled signal after low pass and high pass filter,WithIt is respectively、'sPoint DFT；
Step 4, general,It is updated to
Can obtainPoint sequence?Discrete fractional Brownian random field during rank；
Step 5, useWithAssociation list is shown asIt is one-dimensional subband Fractional Fourier Transform formula,WithIt is referred to as correlation factor；
If step 6 signalEnergy be concentrated mainly on frequency bandIn addition, XaK () can be approximated to beHere,It isApproximate expression, i.e. approximation subband Fourier Transform of Fractional Order.
Below it is only in fractional order territory, one-dimensional sequence to be done height-low frequency decompose.In aforementioned manners subband Fourier Transform of Fractional Order can also be decomposed into more subband
When using two dimension approximation subband Fourier Transform of Fractional Order and filial generation to decompose, image is processed, comprises the following steps:
Step 1, use two dimension chirp signal are to image sequenceIt is modulated, obtains new image sequence；WillBeing divided into four submatrixs, each submatrix hasLength scale
Here,、、、It isRespectively by sequence after Methods of Subband Filter Banks；
Step 2, above-mentioned equation group are write as matrix form and are:
；
It isThe vector space of four sub-sequences composition,It is four filter vector spaces,Be absolute value be all the real number vector space of 1；
,,
Step 3, by simple matrix operations, can obtainMatrix, byMatrix and two-dimensional discrete Fractional Fourier Transform formula
Wherein
Can obtainDuring rankTwo-dimensional sub-band Fourier Transform of Fractional Order
Wherein,,,,It is respectively,,,Two-dimentional Fourier Transform of Fractional Order；
Transformation results is divided into by step 4, subband Fourier Transform of Fractional Order in fractional order territory: low-low frequency, low-high frequency, height-low frequency and four subbands of height-high frequency, when we are rightDo two dimension Fourier Transform of Fractional Order time, i.e.Fractional order territory be divided into four subbands, asEnergy is concentrated mainly on low frequency regionTime, can obtainDuring rankApproximation two-dimensional sub-band Fourier Transform of Fractional Order
。
Below in conjunction with two example laboratory and data result:
(1) selecting ' Lena ' image and ' Cameraman ' image, size is all and is；We have a go at 2-D SB-FrFT when decomposed class is respectively 1,2, and acquiescence selects low-low frequency subband using as rebuilding image.Figure 1It is ' Lena ' original image,Figure 2It is that Lena image does exponent number is Fractional Fourier Transform when 0.4,0.6, fromIn figureUnderstanding, the image energy overwhelming majority concentrates on low-low frequency part, demonstrates original image and concentrates feature in transform domain Energy distribution after two dimension chirp signal modulation.Figure 3Being 0.3, half-band SB-DFrFT during 0.6 exponent number, Half-band refers to here。Figure 4 、 5, 6 distribution beTime SB-DFrFT image reconstruction, there it can be seen that being continuously increased along with decomposed class, after image reconstruction, quality is the most worse and worse, therefore should select suitable decomposed class in practical operation.Table 1Giving SB-FFT and SB-DFrFT parameter comparison in terms of image reconstruction, we carry out the feasibility of evaluation algorithms by mean square error and rebuild the quality of image here.
Table 1The complexity of different mapping algorithms and SNR
(2) we select ieee standard image library ' Baboo ', ' Lena ', ' Camera ' three width image carries out simulating, verifying.Image is carried out 8 × 8 or 16 × 16 piecemeals, the most each data block is carried out SB-DFrFT, owing to image overwhelming majority energy concentrates on low frequency part, hence with ZigZag principle, retain and comprise the bigger pixel of energy, remaining zero setting.Once we respectively with FrFT andSB-DFrFT above three width images are done compression emulation.Figure 6Give the compression of images performance of FrFT algorithm, whereinFigure7,8 is the PSNR value under 0-1 exponent number and CR value, and step-length is 0.01, when exponent number is 1, is DFT compression performance, it can be seen that FrFT is better than common Fourier property in terms of Y-PSNR, but the compression ratio of incomparable DFT.
Figure 7GiveThe compression of images performance of SB-DFrFT algorithm.Understanding, compression method based on SB-DFrFT, compared with FrFT algorithm, all improves a lot in compression ratio (CR) and Y-PSNR (PSNR) aspect, improves 7dB as PSNR value is maximum, and CR maximum improves 2 times.This is owing to first SB-DFrFT algorithm extracts the low-frequency information of image, then utilizes ZigZag to again reduce the redundancy of image.And, we utilize and also attempt utilizing SB-DFrFT to process whole image, obtain being to the maximum the Y-PSNR of 40dB, but compression ratio maximum is only 4.Finally,Table 2Give the elapsed time of FrFT, SB-DFrFT and DCT algorithm, fromIn tableUnderstand, based on SB-DFrFT algorithm than FrFT algorithm fast 16 times, and than DCT algorithm fast about 3 times.
2 three kinds of algorithms of table time-consumingly contrast [sec]Table 2
| [0083] | [0084] FrFT | [0085] SB-FrFT(q=1) | [0086] DCT |
| [0087] Baboo | [0088] 11.973 | [0089] 0.813 | [0090] 2.53 |
| [0091] Camera | [0092] 12.142 | [0093] 0.797 | [0094] 2.54 |
| [0095] Lena | [0096] 11.439 | [0097] 0.86 | [0098] 2.53 |
Claims (2)
1. one kind based on Fourier Transform of Fractional Order and the image processing method of sub-band division, it is characterised in that: use the subband fraction Fourier conversion of one-dimensional approximation that image is processed, comprise the following steps:
Step 1, by a length ofThe sequence of (even number), being decomposed into length is'sWithTwo sequences,,,Can be obtained fom the above equation,；
Step 2, settingIt isApproximate part, be equivalent toBy a low pass filter；It isDetail section, be equivalent toBy a high pass filter；The frequency respectively allowed in half frequency band due to two wave filter is passed through, so just decomposing a sequence into the set of two band limit components；
Step 3, continuation are decomposed, and image is progressively decomposed into the set of multiple band limit component；It is respectively2 times-down-sampled signal after low pass and high pass filter,WithIt is respectively、'sPoint DFT；
Step 4, general,It is updated to
Can obtainPoint sequence?Discrete fractional Brownian random field during rank；
Step 5, useWithAssociation list is shown asIt is one-dimensional subband Fractional Fourier Transform formula,WithIt is referred to as correlation factor；
If step 6 signalEnergy be concentrated mainly on frequency bandIn addition, XaK () can be approximated to beHere,It isApproximate expression, i.e. approximation subband Fourier Transform of Fractional Order.
2. one kind based on Fourier Transform of Fractional Order and the image processing method of sub-band division, it is characterised in that: two dimension approximation subband Fourier Transform of Fractional Order can also be used, comprise the following steps:
Step 1, use two dimension chirp signal are to image sequenceIt is modulated, obtains new image sequence；WillBeing divided into four submatrixs, each submatrix hasLength scale
Here,、、、It isRespectively by sequence after Methods of Subband Filter Banks；
Step 2, above-mentioned equation group are write as matrix form and are:
；
It isThe vector space of four sub-sequences composition,It is four filter vector spaces,Be absolute value be all the real number vector space of 1；
,,
Step 3, by simple matrix operations, can obtainMatrix, byMatrix and two-dimensional discrete Fractional Fourier Transform formula
Wherein
Can obtainDuring rankTwo-dimensional sub-band Fourier Transform of Fractional Order
Wherein,,,,It is respectively,,,Two-dimentional Fourier Transform of Fractional Order；
Transformation results is divided into by step 4, subband Fourier Transform of Fractional Order in fractional order territory: low-low frequency, low-high frequency, height-low frequency and four subbands of height-high frequency, when we are rightDo two dimension Fourier Transform of Fractional Order time, i.e.Fractional order territory be divided into four subbands, asEnergy is concentrated mainly on low frequency regionTime, can obtainDuring rankApproximation two-dimensional sub-band Fourier Transform of Fractional Order
。
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| US4601006A (en) * | 1983-10-06 | 1986-07-15 | Research Corporation | Architecture for two dimensional fast fourier transform |
| CN104361570A (en) * | 2014-11-19 | 2015-02-18 | 深圳市富视康实业发展有限公司 | Image fusing method based on fractional Fourier transformation |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110335298A (en) * | 2019-07-11 | 2019-10-15 | 史彩成 | One kind being based on unmanned aerial vehicle platform image racemization method |
| CN110335298B (en) * | 2019-07-11 | 2021-08-24 | 史彩成 | Image despinning method based on unmanned aerial vehicle platform |
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Application publication date: 20161123 |