CN104200442B - Non-local mean MRI image denoising method based on improved canny rim detections - Google Patents
Non-local mean MRI image denoising method based on improved canny rim detections Download PDFInfo
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Abstract
The invention discloses a kind of non-local mean MRI image denoising method based on improved canny rim detections, including：(1) squared magnitude processing is carried out to MRI image and obtains squared magnitude image；(2) noise is estimated；(3) edge of squared magnitude image is extracted using canny operators；(4) edge/intensity similarity calculated between two similar blocks is estimated；(5) weight parameter is calculated；(6) non-local mean method is handled；(7) deviation is corrected.The present invention is advantageous in that：Due to considering the marginal likelihood between similar block simultaneously, using improved canny edge detecting technologies, overcome the distance between similar block in traditional NLM methods and only rely on the drawbacks of single parameter of image pixel intensities carries out weight parameter calculating, so that similarity measurement is more accurate, and then improve the effect of image denoising；Employ non-local mean filtering and replace gaussian filtering, preferably maintain edge, and eliminate part noise, make rim detection more accurate.
Description
Technical field
The present invention relates to a kind of image de-noising method, and in particular to a kind of non-office based on improved canny rim detections
Portion's average MRI image denoising method, belongs to technical field of image processing.
Background technology
In recent years, with the development of magnetic resonance imaging (magnetic resonance images, MRI) technology, the mankind couple
The ability of brain research has obtained unprecedented raising, at the same time generates substantial amounts of MRI image.Passed through in the acquisition process of MRI image
Different noise jammings is subjected to, research is found, Rician distributions are mainly presented in the noise in MRI image.
MRI image has been widely used for medical diagnosis at present, its corresponding processing for noise existing for current MRI image
Technology also have it is a variety of, wherein popular has anisotropy parameter Denoising Algorithm, total variation Denoising Algorithm, non-local mean Denoising Algorithm
Deng.
The characteristics of model of anisotropy parameter Denoising Algorithm itself, determines the defects of it is present.When image is dirty by very noisy
During dye, gradient caused by noise is likely to the gradient more than image detail edge, and at this moment the model can not correctly distinguish noise
And detail edges, so as to which noise can not be removed well.
Total variation Denoising Algorithm finds a kind of equilibrium state between the TV norms of image and loyal item, i.e., energy functional is minimum
Value, but when the parameter lambda very little in energy functional, the small minutia of the image as texture will be destroyed.
There is following shortcoming for non-local mean Denoising Algorithm：(1) algorithm complex is big, calculates time length；(2) similar window
Measuring similarity function only account for the intensity similarity of pixel, the accuracy of pixel weight distribution has much room for improvement；(3) part
Parameter chooses excessively sensitivity, lacks perfect theoretical direction；(4) there is deviation in non-local mean denoising, in actual applications should
This is corrected.
The content of the invention
For solve the deficiencies in the prior art, it is an object of the invention to provide one kind based on improved canny rim detections,
It can effectively, accurately remove the non-local mean MRI image denoising method of MRI image noise.
In order to realize above-mentioned target, the present invention adopts the following technical scheme that：
A kind of non-local mean MRI image denoising method based on improved canny rim detections, it is characterised in that bag
Include following steps：
Step 1, squared magnitude processing is carried out to the MRI image containing Rician noises, obtains squared magnitude image；
Step 2, the background area of squared magnitude image is chosen, the noise estimation expression formula provided according to formula (1) is made an uproar
Sound is estimated：
In formula, μ is the pixel average of selected background area in magnitude image Square Graphs picture, and σ is noise variance；
Step 3, the edge of squared magnitude image is extracted using canny operators：
(1) filter：Smothing filtering is carried out to squared magnitude image using the non-local mean wave filter of classics；
(2) Grad and gradient direction angle are calculated：Amplitude Square Graphs are as in X-direction and Y-direction after asking for filtering respectively
Gradient MxAnd My, according to aforementioned gradient MxAnd MyCalculate the Grad of squared magnitude image | △ f | with gradient direction angle θ：
It is 4 directions by 0 °~360 ° gradient direction angle merger：0 °, 45 °, 90 °, 135 °；
(3) non-maximum suppresses：The pixel on gradient direction with greatest gradient value is retained as edge pixel, will
Other pixels are deleted；
(4) hysteresis threshold：Set a high threshold thighWith a Low threshold tlow, according to pixel gradient value and high threshold
Value thigh, Low threshold tlowRelation carry out marker edge pixel；
Step 4, similarity measure is calculated：
The similar block that size is 5 × 5 is chosen, edge extraction and detection are carried out in the range of 11 × 11, if squared magnitude
The intensity of certain point is I (x, y) on image, the amplitude of the certain point in squared magnitude image on edge image for Canny (x,
Y), wherein, x, y are some pixel i positions,
Marginal likelihood between two similar blocks estimates D1Provided by formula (4)：
D1=| | Canny (Ni)-Canny(Nj)||2,bFormula (4)
In formula, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, b is the Gaussian kernel weighting that standard deviation is b；
Intensity similarity between two similar blocks estimates D2Provided by formula (5)：
In formula, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, a is the Gaussian kernel weighting that standard deviation is a；
Step 5, weight parameter calculates：
Estimate D with reference to the intensity similarity between two similar blocks calculated in step 42And edge similar degree estimates D1,
Form new weight calculation expression formula：
In formula, h is filtering parameter, and h' is edge filter parameter, and Z (i) is global normalization's function,
Step 6, non-local mean method is handled：
Formula (7) is performed to each pixel in the squared magnitude image of the noise containing Rician：
Wherein, 0≤w (i, j)≤1, Y (i) is pixel i intensity, and Y (j) is pixel j intensity,Time
Go through entire image and obtain the image after the processing of non-local mean method；
Step 7, deviation is corrected：
The denoising image obtained to step 6 carries out drift correction, and image S is obtained by expression after final denoising：
I (i) is pixel i intensity.
The foregoing non-local mean MRI image denoising method based on improved canny rim detections, it is characterised in that
In step 2, the background area of squared magnitude image is chosen using Ostu threshold techniques.
The foregoing non-local mean MRI image denoising method based on improved canny rim detections, it is characterised in that
In step 3, the process of filtering is：
1., choose size be 5 × 5 similar block, searched in the range of 11 × 11, if a certain on squared magnitude image
The intensity of point is I (x, y), and the intensity similarity between two similar blocks estimates D2For：
In formula, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, a is the Gaussian kernel weighting that standard deviation is a；
2., calculate weight w (i, j)：
In formula, h is filtering parameter, and Z (i) is global normalization's function,
3., in the image of the noise containing Rician each pixel perform formula (7)：
Wherein, 0≤w (i, j)≤1,Y (i) is pixel i intensity, and Y (j) is pixel j intensity, time
Go through entire image；
4., drift correction is carried out to the image that 3. obtains, obtain the filtered image of non-local mean：
I (i) is pixel i intensity.
The foregoing non-local mean MRI image denoising method based on improved canny rim detections, it is characterised in that
In step 3, Grad is asked to carry out convolution completion using Sobel Operator template and image, wherein,
The foregoing non-local mean MRI image denoising method based on improved canny rim detections, it is characterised in that
In step 3, according to pixel gradient value and high threshold thigh, Low threshold tlowRelation carry out the method for marker edge pixel and be：
(1) pixel (x, y) Grad is less than tlow, then pixel (x, y) is non-edge pixels；
(2) pixel (x, y) Grad is more than thigh, then pixel (x, y) is edge pixel；
(3) pixel (x, y) Grad is in tlowWith thighBetween, further check pixel (x, y) 3 × 3 neighborhoods, neighborhood
Pixel gradient, which exists, is more than thigh, then (x, y) is edge pixel；
(4) pixel gradient value is not had to be more than t in 3 × 3 neighborhoods of pixel (x, y)high, further expand hunting zone to 5
Pixel, which whether there is, in × 5 neighborhoods is more than thigh, if so, then (x, y) is edge pixel, it is otherwise non-edge pixels.
The present invention is advantageous in that：
1st, for image de-noising method of the invention due to considering the marginal likelihood between similar block simultaneously, use is improved
Canny edge detecting technologies, overcome the distance between similar block in traditional NLM methods and only rely on the single parameter of image pixel intensities and
The drawbacks of row weight parameter calculates so that similarity measurement is more accurate, and then improves the effect of image denoising.
2nd, image de-noising method of the invention is due to considering in canny operator edge detections using gaussian filtering to image
Caused blooming, employ non-local mean filtering and replace gaussian filtering, preferably maintain edge, and eliminate portion
Divide noise, make rim detection more accurate.
3rd, the actual deviation of image de-noising method of the invention due to considering denoising image simultaneously, to squared magnitude image
Carry out it is expected to calculate, estimated deviation, existing deviation is corrected in the image basis after NLM denoisings,
So that the accuracy of denoising is higher, effect is more preferable.
Brief description of the drawings
Fig. 1 is the detail flowchart of the image de-noising method of the present invention.
Embodiment
Make specific introduce to the present invention below in conjunction with the drawings and specific embodiments.
Reference picture 1, the non-local mean MRI image denoising method bag of the invention based on improved canny rim detections
Include following steps：
Step 1, squared magnitude processing is carried out to the MRI image containing Rician noises
MRI image is typically considered to be polluted by the additive white Gaussian noise for being easy to remove, and is actually existed in
Noise in MRI image is not simple additive white Gaussian noise, but the complexity into L-S distribution related to signal is made an uproar
Sound.
MRI image is rebuild by carrying out inverse Fourier transform to the signal of measurement.Raw MRI data is by complexity
Gaussian noise pollutes, during by inverse Fourier transform to image reconstruction, due to the orthogonality of Fourier transformation, image
Noise characteristic not change.Therefore the noise in image after rebuilding is still complicated white Gaussian noise.
Complicated MRI data can be expressed as：
X=XRe+jXIm
In formula, XReFor the real part of data, XImIt is independent by ξ for imaginary part, this two parts1,ξ2Influence, wherein ξ1,ξ2Respectively
Additive white Gaussian noise with zero-mean and standard deviation sigma.
XRe=Scos θ+ξ1
XIe=Ssin θ+ξ2
In formula, S represents original image, and θ is phase.
One secondary noisy image can be expressed as：
It can be found that | x | distribution become L-S distribution, can be expressed as：
In formula, I0Represent single order modified Bessel function, S is no noise cancellation signal, σ2For noise variance, X is MRI magnitude images.
Magnitude image | x | noise estimation be a difficult task, Nowak researchs show that squared magnitude can will
Deviation in MRI image becomes additivity and unrelated with signal.
Calculate | x |2Expectation it is as follows：
E[|X|2]=E [(Scos θ+ξ1)2+(Ssinθ+ξ2)2]=μs 2+2σ2
Therefore in square magnitude image, deviation is 2 σ2。
Step 2, noise is estimated
Noise estimation in MRI image is from the background area of image.Noise estimates that expression formula is：
In formula, μ is the pixel average of selected background area in squared magnitude image, and σ is noise variance.
The selection of background area is carried out using Ostu threshold techniques, here we assume that the pixel of background area is unrelated
, arise primarily at noise.
Step 3, edge detection process
Improved canny operator edge detections are applied in squared magnitude image with abstract image edge.
(1) filter
Smothing filtering is carried out to image using the non-local mean wave filter of classics.The detailed process of filtering is：
1., choose size be 5 × 5 similar block, searched in the range of 11 × 11, if a certain on squared magnitude image
The intensity of point is I (x, y), and the intensity similarity between two similar blocks estimates D2(in i.e. traditional NLM methods two similar blocks it
Between distance measure) be：
In formula, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, a is the Gaussian kernel weighting that standard deviation is a.
Intensity similarity estimates D2In introduce Gaussian kernel weighting, it is therefore intended that distribute bigger weight to center pixel.
2., weight calculation expression formula：
In formula, h is filtering parameter, and Z (i) is global normalization's function,
3., in the image of the noise containing Rician each pixel perform formula (7)：
Wherein, 0≤w (i, j)≤1, Y (i) is pixel i intensity, and Y (j) is pixel j intensity,Time
Go through entire image.
4., to 3. obtain image carry out drift correction, obtain the filtered image of non-local mean：
I (i) is pixel i intensity.
Canny edge detection algorithms gaussian filtering smoothed image, is disadvantageous in that, is removing noise suppressed details
Edge is also obscured simultaneously.Experiment shows the method that gaussian filtering smoothed image is replaced using bilateral filtering, can obtain preferably
Effect.But either gaussian filtering or bilateral filtering, denoising effect are all not so good as non local average filter.Therefore non-office is used
The improved edge detection algorithm of mean filter smoothed image, can be truly compared with traditional Canny edge detection methods
Detect the edge of strong noise image.
(2) Grad and gradient direction angle are calculated
Gradient M of the filtered image in X-direction and Y-direction is asked for respectivelyxAnd My。
Grad is asked to carry out convolution completion using Sobel Operator template and image.Wherein gradient MxAnd MyRespectively：
Grad is：
Gradient direction angle is：
It is 4 direction θ ' by 0 °~360 ° gradient direction angle merger：0°,45°,90°,135°.
For all edges, 180 °=0 °, 225 °=45 ° etc. is allowed.So direction is in [- 225 °~22.5 °] and [157.5 °
~202.5 °] in the range of angle be all integrated into 0 ° of deflection, other angle merger are by that analogy.
(3) non-maximum suppresses
According to Canny on edge detection operator performances evaluation criterion, edge only allows the width for having a pixel, and real
After Soble is filtered, the edge thickness in image is different on border.Edge thickness depends primarily on the density of bounding edge
Distribution and the fog-level using image after gaussian filtering.
Non- maximum suppresses, and is that the pixel with greatest gradient value is protected as edge pixel on gradient direction using those
Stay, other pixels are deleted.
Maximum of gradients is generally present in the center at edge, and with the increase along gradient direction distance, Grad will therewith
Reduce.
With reference to the Grad and deflection of obtained each pixel, the pixel in the range of the 3 × 3 of point (x, y) is checked：
| θ ' (x, y) value | Required inspection pixel | Pixel retains and meets condition |
| 0° | (x+1,y),(x,y),(x-1,y) | (x+1,y)<(x,y)>(x-1,y) |
| 90° | (x,y+1),(x,y),(x,y-1) | (x,y+1)<(x,y)>(x,y-1) |
| 45° | (x+1,y+1),(x,y),(x-1,y-1) | (x+1,y+1)<(x,y)>(x-1,y-1) |
| 135° | (x+1,y-1),(x,y),(x-1,y+1) | (x+1,y-1)<(x,y)>(x-1,y+1) |
(4) hysteresis threshold
The reason for noise is present, often occurring continuously breakage problem should occurs in edge.Hysteresis thresholdization setting two
Individual threshold value, a high threshold thighOne Low threshold tlow.Response of the pixel to boundary operator exceedes high threshold, by element marking
For edge；Response exceedes Low threshold (between high-low threshold value), if abutted with labeled pixel 4- adjoinings or 8-, these
Pixel is also indicated as edge.Iterate, remaining isolated response is then considered as noise more than the pixel of Low threshold, not existed
Labeled as edge.Detailed process is as follows：
Pixel 1. (x, y) Grad is less than tlow, then pixel (x, y) is non-edge pixels；
Pixel 2. (x, y) Grad is more than thigh, then pixel (x, y) is edge pixel；
Pixel 3. (x, y) Grad is in tlowWith thighBetween, further check pixel (x, y) 3 × 3 neighborhoods, neighborhood picture
Plain gradient, which exists, is more than thigh, then (x, y) is edge pixel；
4. there is no pixel gradient value to be more than t in 3 × 3 neighborhoods of pixel (x, y)high, further expansion hunting zone to 5 ×
Pixel, which whether there is, in 5 neighborhoods is more than thigh, if so, then (x, y) is edge pixel, it is otherwise non-edge pixels.
Step 4, similarity measure is calculated
The similar block that size is 5 × 5 is chosen, edge extraction and detection are carried out in the range of 11 × 11, if squared magnitude
The intensity of certain point is I (x, y) on image, the amplitude of the certain point in squared magnitude image on edge image for Canny (x,
y)。
Marginal likelihood between two similar blocks estimates D1Provided by formula (4)：
D1=| | Canny (Ni)-Canny(Nj)||2,bFormula (4)
Wherein, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, b is the Gaussian kernel weighting that standard deviation is b.
Intensity similarity between two similar blocks estimates D2(the distance between two similar blocks in i.e. traditional NLM methods
Estimate) provided by formula (5)：
Wherein, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, a is the Gaussian kernel weighting that standard deviation is a.
Marginal likelihood between two similar blocks is estimated, intensity similarity estimate introduce Gaussian kernel weighting, purpose
It is to distribute bigger weight to center pixel.
Step 5, weight parameter calculates
Estimate D with reference to the intensity similarity between two similar blocks calculated in step 42And edge similar degree estimates D1,
Form new weight calculation expression formula：
Wherein, h is filtering parameter, and h' is edge filter parameter, and Z (i) is global normalization's function,
Step 6, non-local mean method is handled
Combined by the weight parameter and traditional non-local mean method (NLM) that are obtained in step 5, image is carried out at NLM
Reason.Formula (7) is performed to each pixel in noise image containing Rician：
Wherein, 0≤w (i, j)≤1,Y (i) is pixel i intensity, and Y (j) is pixel j intensity, time
Go through entire image, you can obtain the image after NLM processing.
Step 7, deviation is corrected
The denoising image obtained to step 6 carries out drift correction, and image S is obtained by expression after final denoising：
I (i) is pixel i intensity.
To being compensated and corrected on square magnitude image using deviation caused by NLM methods, in the image that step 6 obtains
Each pixel on perform amendment 2 σ2Deviation, so as to finally give the good MRI image of denoising effect.
By using the denoising result that is obtained of denoising method of the present invention and existing non-local mean (NLM) and its
The experimental result of improved method is analyzed, and comparing result is as follows：
The SSIM of table 1 qualitative comparing result
Table 2 Y-PSNR PNSR (dB) quantitative contrast result
Analysis result shows that the denoising result that method of the invention obtains is substantially better than other several methods, experiment effect
Lifting is obvious.
The MRI image of multi-coil collection simultaneously disobeys L-S distribution, therefore the method for the present invention is only for using unicoil
Obtain the situation of MRI image.
It should be noted that the invention is not limited in any way for above-described embodiment, it is all to use equivalent substitution or equivalent change
The technical scheme that the mode changed is obtained, all falls within protection scope of the present invention.
Claims (5)
1. the non-local mean MRI image denoising method based on improved canny rim detections, it is characterised in that including following
Step：
Step 1, squared magnitude processing is carried out to the MRI image containing Rician noises, obtains squared magnitude image；
Step 2, the background area of squared magnitude image is chosen, the noise estimation expression formula provided according to formula (1) carries out noise and estimated
Meter：
In formula, μ is the pixel average of selected background area in squared magnitude image, and σ is noise variance；
Step 3, the edge of squared magnitude image is extracted using canny operators：
(1) filter：Smothing filtering is carried out to squared magnitude image using the non-local mean wave filter of classics；
(2) Grad and gradient direction angle are calculated：Ask for respectively filtering after amplitude Square Graphs picture X-direction and Y-direction gradient Mx
And My, according to the gradient MxAnd MyCalculate the Grad of squared magnitude image | △ f | with gradient direction angle θ：
It is 4 directions by 0 °~360 ° gradient direction angle merger：0 °, 45 °, 90 °, 135 °；
(3) non-maximum suppresses：The pixel on gradient direction with greatest gradient value is retained as edge pixel, will be other
Pixel is deleted；
(4) hysteresis threshold：Set a high threshold thighWith a Low threshold tlow, according to pixel gradient value and high threshold
thigh, Low threshold tlowRelation carry out marker edge pixel；
Step 4, similarity measure is calculated：
The similar block that size is 5 × 5 is chosen, edge extraction and detection are carried out in the range of 11 × 11, if squared magnitude image
The intensity of upper certain point is I (x, y), and the amplitude of the certain point in squared magnitude image on edge image is Canny (x, y), its
In, x, y are some pixel i positions,
Marginal likelihood between two similar blocks estimates D1Provided by formula (4)：
D1=| | Canny (Ni)-Canny(Nj)||2,bFormula (4)
In formula, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, b is the Gaussian kernel weighting that standard deviation is b；
Intensity similarity between two similar blocks estimates D2Provided by formula (5)：
In formula, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, a is the Gaussian kernel weighting that standard deviation is a；
Step 5, weight parameter calculates：
Estimate D with reference to the intensity similarity between two similar blocks calculated in step 42And edge similar degree estimates D1, formed
New weight calculation expression formula：
In formula, h is filtering parameter, and h' is edge filter parameter, and Z (i) is global normalization's function,
Step 6, non-local mean method is handled：
Formula (7) is performed to each pixel in the squared magnitude image of the noise containing Rician：
Wherein, 0≤w (i, j)≤1, Y (i) is pixel i intensity, and Y (j) is pixel j intensity,Travel through whole
Width image obtains the image after the processing of non-local mean method；
Step 7, deviation is corrected：
The denoising image obtained to step 6 carries out drift correction, and image S is obtained by expression after final denoising：
if NLM(I(i))≥2σ2
The else of S (i)=0
I (i) is pixel i intensity.
2. the non-local mean MRI image denoising method according to claim 1 based on improved canny rim detections,
Characterized in that, in step 2, the background area of squared magnitude image is chosen using Ostu threshold techniques.
3. the non-local mean MRI image denoising method according to claim 1 based on improved canny rim detections,
Characterized in that, in step 3, the process of filtering is：
1., choose the similar block that size is 5 × 5, searched in the range of 11 × 11, if certain point on squared magnitude image
Intensity is I (x, y), and the intensity similarity between two similar blocks estimates D2For：
In formula, NiFor the neighborhood of ith pixel, NjFor the neighborhood of j-th of pixel, a is the Gaussian kernel weighting that standard deviation is a；
2., calculate weight w (i, j)：
In formula, h is filtering parameter, and Z (i) is global normalization's function,
3., in the image of the noise containing Rician each pixel perform formula (7)：
Wherein, 0≤w (i, j)≤1,Y (i) is pixel i intensity, and Y (j) is pixel j intensity, and traversal is whole
Width image；
4., drift correction is carried out to the image that 3. obtains, obtain the filtered image of non-local mean：
if NLM(I(i))≥2σ2
I (i) is pixel i intensity.
4. the non-local mean MRI image denoising method according to claim 1 based on improved canny rim detections,
Characterized in that, in step 3, ask Grad to carry out convolution completion using Sobel Operator template and image, wherein,
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5. the non-local mean MRI image denoising method according to claim 1 based on improved canny rim detections,
Characterized in that, in step 3, according to pixel gradient value and high threshold thigh, Low threshold tlowRelation carry out marker edge pixel
Method be：
(1) pixel (x, y) Grad is less than tlow, then pixel (x, y) is non-edge pixels；
(2) pixel (x, y) Grad is more than thigh, then pixel (x, y) is edge pixel；
(3) pixel (x, y) Grad is in tlowWith thighBetween, further 3 × 3 neighborhoods of inspection pixel (x, y), neighborhood territory pixel are terraced
Degree, which exists, is more than thigh, then (x, y) is edge pixel；
(4) pixel gradient value is not had to be more than t in 3 × 3 neighborhoods of pixel (x, y)high, further expand hunting zone to 5 × 5 neighbours
Pixel, which whether there is, in domain is more than thigh, if so, then (x, y) is edge pixel, it is otherwise non-edge pixels.
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