CN106469438B - Neighborhood based on card side's unbiased esti-mator shrinks MRI denoising method - Google Patents
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Abstract
A kind of neighborhood shrinkage de-noising method based on card side's unbiased esti-mator for this noise of MRI Lay of disclosure of the invention.The step of this method is after estimation noise criteria is poor, to after noise image square divided by square of noise criteria difference, to meet the property of non-central chi square distribution, then not normalized steady haar wavelet transform is carried out, high and low frequency coefficient is obtained, to low frequency coefficient two-sided filter deblurring, to neighborhood shrinkage method of the high frequency coefficient based on card side's unbiased esti-mator, cyclic shift is carried out to the wavelet coefficient after denoising, several are finally shifted into denoising image and is averaging to obtain denoising image.
Description
Technical field
The invention belongs to technical field of image processing.It particularly relates to it is a kind of to remove this noise of MRI Lay, improve letter
The neighborhood based on card side's unbiased esti-mator than for the purpose of of making an uproar shrinks MRI denoising method.
Background technique
In modern medicine, magnetic resonance imaging (MRI) medical imaging technology basic as one has become doctor and examines
Disconnected and treatment important supplementary means, magnetic resonance image are made an uproar in acquisition process since the factor of hardware circuit and human body can introduce
Sound, noise reduce the quality of MRI, so that the boundary of some tissues thickens, fine structure is difficult to distinguish, increase to figure
As the discriminance analysis of details and the difficulty of processing, medical diagnosis is influenced.It therefore, is a reality for the denoising of noise MRI software
With convenient and high cost performance thing.
Common MRI acquisition methods are sampled to interested target in frequency domain (domain k), then to frequency domain number
According to inverse discrete fourier transform is carried out, the complex image data comprising real and imaginary parts is obtained, amplitude data is reconverted into, in reality
After being converted into magnitude image, Lay this (Rician) distribution is presented in the additive white Gaussian noise that portion and imaginary part introduce.When noise compares
Gao Shi, L-S distribution tend to Gaussian Profile, when signal-to-noise ratio is low, it is intended to rayleigh distributed, therefore for low signal-to-noise ratio
MRI, biggish deviation can be generated by carrying out noise estimation and denoising with the method for traditional removal Gaussian noise.
Currently, in MRI denoising a major issue be retain useful edge, detailed information because medical image concerning
Patient safe, any small fault do not allow.Usually there are three types of modes for MRI denoising, first is that being directed to Lay in amplitude domain
The model denoising of this distribution also has the MRI to three-dimensional to be denoised second is that square domain in amplitude denoises.Nowak in 1999
It proposes, square noise image is made to produce unrelated with signal, additivity a biasing, this is biased in ruler after wavelet transformation
Retain in degree coefficient, denoising effect can be promoted by directly subtracting biasing, and square magnitude image obeys the non-of two freedom degrees
Center chi square distribution.The scale coefficient of square image is removed biasing by Nowak, to the property of high-frequency wavelet coefficient chi square distribution
Signal variance is calculated, the point-by-point ratio contraction method of similar Wiener filtering is reapplied, obtains the denoising shunk better than Traditional Wavelet
Effect.Anand et al. (2010) is on the basis of Nowak, by square magnitude image after Stationary Wavelet Transform, height frequency division
Not Cai Yong NeighShrinkSURE and two-sided filter denoised, the processing to high frequency coefficient be no longer handle point by point, but
Consider the neighborhood of pixel.In low frequency coefficient, containing most image energy, signal-to-noise ratio is high, and two-sided filter is good
Holding edge ability, can preferably filter out noise with deblurring, this method.Luisier et al. (2012) is in paper
" CURE for noisy Magnetic Resonance Imgaes:Chi-square unbiased risk
Estimation " be directed to square MRI non-central chi square distribution model, derive for chi square distribution mean square error it is unbiased
Estimated expression (CURE) is applied in two kinds of linear threshold extensions denoising method (LET), and one is that the CURE of image area estimates
Determine the LET parameter under wavelet field UWT transformation, secondly the parameter of the LET to estimate determining wavelet field with the CURE of wavelet field, by
It can be only applied to not normalized Ha Er (Haar) small echo in the CURE estimation of the special nature of non-central chi square distribution, wavelet field
Transformation.
Summary of the invention
In order to remove noise, the signal-to-noise ratio of MRI is improved, the present invention, which has been derived, is only dependent upon the threshold of wavelet coefficient in wavelet field
It is worth the CURE estimated expression of contraction method, allows to be suitable on neighborhood shrinkage de-noising method, in conjunction with the double of low frequency part
Side filter process and quick cyclic shift technique achieve preferable MRI denoising effect.
Neighborhood based on card side's unbiased esti-mator shrinks MRI denoising method, includes the following steps:
(1) noise criteria difference σ is estimated in the background area of MRI；
(2) to noise image m progress square, then divided by square of noise criteria difference σ, image y is obtained
(3) not normalized steady haar wavelet transform (SWT) is carried out to y, decomposes L layers, obtains high frequency coefficient and low frequency system
Number, high frequency coefficient have L*3 subband；
(4) to low frequency coefficient two-sided filter deblurring, neighborhood of the high frequency coefficient based on card side's unbiased esti-mator is received
Contracting method (NeighShrinkCURE) denoising；
(5) cyclic shift, inverse wavelet transform (ISWT) are carried out together with low frequency coefficient to the wavelet coefficient after denoising, if obtaining
The denoising result of dry cyclic shift；
(6) denoising result of above-mentioned several cyclic shifts is obtained into final denoising figure by Nonlinear Mapping, averaging
Picture.
The NeighShrinkCURE includes two parts, one is the threshold value depending on wavelet coefficient of wavelet field
The derivation of the CURE estimated expression of contraction method, the second is the calculating of the CURE estimated value of neighborhood contraction method.
1, wavelet field is as follows about the derivation process of the CURE estimated expression of the threshold value contraction method of wavelet coefficient:
If withIndicate a Nx×NyThe index set of the image of size, with μ=[μn]n∈Ω∈CNIndicate reason
Think that the size (without making an uproar) is N=Nx×NyMR complex image, m=[mn]n∈Ω∈CNIndicate the MR image of Noise, Denoising Problems
Be converted to the problem of μ is estimated from m.In MR data acquisition, real and imaginary parts can introduce the Gauss that standard deviation is σ respectively
Noise, statistical property can be stated are as follows:
Expression takes real,It indicates to take plural imaginary part.Our target is estimation μnAmplitude,It is as follows to define x and y:
Then y obeys non-central chi square distribution,Non-centrality parameter is x, freedom degree K=2, Denoising Problems
The problem of non-centrality parameter x is estimated from the data y of non-central chi square distribution can be converted to again.Function f (y) is denoised in design
Come when estimating x, a natural evaluation criterion is mean square error (MSE):
Needed as can be seen that calculating MSE without noise cancellation signal x from formula, this in actual conditions be it is unforeseen, whenThat is it is x that y, which obeys non-centrality parameter, and when freedom degree is K, Luisier et al. is according to the system of non-central chi square distribution
Characteristic is counted, one side's of card unbiased esti-mator (CURE) of unbiased esti-mator of MSE is deduced, as long as f (y) meets continuous or smooth limit
System, so that it may calculate the unbiased esti-mator CURE of MSE by f (y), and be generalized to wavelet field, propose that not normalized Ha Er is small
CURE estimation under wave conversion.This method only considers not normalizing the estimation of the CURE under haar wavelet transform, not normalized Kazakhstan
Your small echo means the scaling function of basic haar wavelet transformWavelet functionAnd
Not normalized Haar wavelet transform scaling function [1,1], wavelet function [1, -1], this is to still meet wavelet coefficient in non-
The property of heart chi square distribution, in inverse wavelet transform, reconstruction filter will also make corresponding change.In Luisier paper
Correlation theorem is stated in this way, is done to image y and is not normalized haar wavelet transform, and the scale coefficient s of jth layer is obtainedjWith it is small
Wave system number wj, with θ (w, s)=θj(wj, sj) indicate to wavelet conversion coefficient ω=ω of no noise cancellation signal xjEstimation, then jth layer
The MSE of wavelet coefficient can be estimated by following formula:
K in formulaj=2jK, K are the freedom degrees of non-central chi square distribution, when magnetic resonance tool unicoil is acquired and is imaged, K
=2.Denoise function and depend on noise wavelet coefficients w, scale coefficient s, and many common Denoising Algorithms such as soft-threshold shrink,
Two variables contraction be all not consider scale coefficient, in the case where not considering scale coefficient, the present invention derive only consider it is small
The CURE of the threshold value contraction method of wave system number w estimates, i.e., replaces θ (w, s) to estimate the wavelet coefficient without noise cancellation signal with θ (w).
To simplify problem, we transform into image one-dimensional signal, and noise signal y, ideal signal x pass through jth layer small echo
Decomposing gained scale coefficient is respectively sj、High frequency coefficient is respectivelyThen basis does not normalize Haar wavelet transform change
The property changed can obtain:
In formulaKj=2jK=2j+1。
The MSE of jth layer wavelet coefficient may be expressed as:
Consider that first layer decomposes j=1, noise signal y=sj-1, ideal signalK=Kj/ 2, then term2 can table
It states are as follows:
E{ωnθn(w) }=E { x2nθn(w)}-E{x2n-1θn(w)} (7)
Luisier is it has been proved that work asWhen f (y) can continuously be led:
It applies formula (6) and asks (5):
Substitute into term2:
It applies formula (10) and seeks term3:
Term1, term2, term3 substitution (8) can must be finally only dependent upon to the small of the threshold value contraction method of wavelet coefficient w
Wave zone CURE estimation:
The decomposition of remainder layer can also obtain similar proof, and the wavelet transformation of two dimensional image is to horizontal and vertical side
To wavelet transformation is done respectively, above-mentioned formula also can directly be generalized to two dimensional image, and the change done is Kj=22·jK。
2, such as above-mentioned after deriving the wavelet field CURE estimation for only considering the threshold method of wavelet coefficient w, it is applied to
In neighborhood shrinkage de-noising method, main problem be threshold function table derivative calculations and threshold function table it is smooth.
Neighborhood shrinkage method considers currently pending wavelet coefficient wijCentered on square neighborhood Bij, give square neighborhood
Coefficient andIf λ is that the global threshold of current wavelet sub-band in order to express easily uses wnIndicate wij, SnIt indicates
Sij, then threshold value shrinkage formula can state are as follows:
In formula, θ (wn) be denoising after wavelet coefficient, optimal threshold value λ, i.e. λ are determined with CURE estimationopt=
ArgminCURE (λ), window size take 3*3, and CURE estimation needs to calculate θ (wn) single order and second-order differential, enableG=max (u, 0), by layering derivation, steps are as follows:
CURE estimation has smooth requirement to denoising function, and g=max (u, 0) must be done smoothly, utilize incomplete βfunction
It does smoothly, if smooth denoising function is g=f (u)=u.*I (u), wherein
In formula, a, b are smooth in order to guarantee for controlling smooth degree
Center of curve is symmetrical, and a, b palpus value are identical, a=b=80.
3, the cyclic shift (Cycle Spinning, CS) is to eliminate and translate since Stationary Wavelet Transform lacks
Invariance and the Pseudo-Gibbs artifacts generated.Traditional cycle spinning (Cycle Spinning) " follows signals and associated noises progress
Ring translation-threshold denoising-reverse circulation translation ".It can make pseudo- gibbs due to carrying out threshold denoising to the signal after each translation
Phenomenon appears in different places, therefore can all obtain a different denoising knot for every group of translational movement on row and column direction
Fruit μI, j, i, j are respectively the translational movement on row and column direction, and carrying out linear averaging to all denoising results will be suppressed pseudo- Ji
The denoising result of Buss phenomenon.However, traditional shift method translates every time will call denoising function, consuming time is long, in order to
Accelerate the speed of service, the present invention considers the cycle spinning just for the wavelet coefficient after denoising, when can greatly save in this way
Between, because the size of each subband of Stationary Wavelet Transform is identical with original image, image translation and the translation on denoising coefficient are influenced
Less, it especially when picture size is larger, only will be different in edge, facts proved that under Stationary Wavelet Transform, it is this
Rapid Circulation shift method with basic skills the result is that as, runing time but greatly reduces.
Detailed description of the invention
Following further describes the present invention with reference to the drawings:
Fig. 1 shrinks MRI denoising method flow chart based on the neighborhood of card side's unbiased esti-mator；
The MSE and CURE of Fig. 2 neighborhood shrinkage method estimate comparison diagram；
The translation of Fig. 3 conventional recycle and Rapid Circulation translate schematic diagram；
Fig. 4 T2w, 7% noise the 40th slice noise, nothing are made an uproar and noise-free picture partial enlarged view
Fig. 5 T2w, 7% noise the 40th slice denoising effect contrast figure, including denoising image, (noise pattern subtracts residual image
Denoising is schemed) and local enlarged drawing.
Fig. 6 T2w, the denoising index comparison of 7% noise the 40th to the 100th slice
The simulation of the slice of Fig. 7 T2w the 40th plus the denoising index comparison of varying strength Rician noise
Specific embodiment
The neighborhood that the present invention provides a kind of based on card side's unbiased esti-mator shrinks MRI denoising method, when needing to noise MRI
When carrying out denoising, following steps are successively executed as shown in Figure 1:
Step 1 estimates noise criteria difference σ in the background area of MRI:
μ is the mean value for the background area pixels value chosen.
Step 2, then divided by square of noise criteria difference σ, obtains image y to noise image m progress square；
Y=m2/σ2 (2)
Step 3 carries out not normalized steady haar wavelet transform to y, decomposes L layers, obtains high frequency coefficient and low frequency coefficient,
High frequency coefficient has L*3 subband；
Step 4 is to low frequency coefficient two-sided filter deblurring；Each subband is used within the scope of scheduled threshold search
The denoising of NeighShrinkCURE method, determines optimal threshold value λ, i.e. λ in threshold range with CURE estimationopt=arg
Min CURE (λ), then useIt is denoised；
Wavelet coefficient after step 5 pair denoising carries out cyclic shift together with low frequency coefficient, and CS=9, i.e., move right i respectively
Position, to moving down j, i ∈ [0,2], j ∈ [0,2], progress inverse wavelet transform, then counter translate corresponding digit and obtain
Step 6 by?
Step 7 is to obtainingThe final denoising image being averaging
Carry out the performance of detailed analysis this method below by three groups of experiments:
From MRI data library (http://brainweb.bic.mni.mcgill.ca/brainweb/) downloading T1 weighting
(T1w), T2 weights 8 bit MRI of the different noise grades of (T2w) and proton density weighting (PD), and initial data is three-dimensional vertical
The brain simulation MRI scan data of body, resolution ratio 181*217*181, by method (NeighShrinkCURE+ of the invention
BF/CS=9) and the two-sided filter of Anand et al. combines the neighborhood shrinkage method based on Stein unbiased esti-mator
(NeighShrinkSURE+BF), the CURE-LET haar/CS=16 method of Luisier et al. compares.
Experiment 1: taking T1w, and the 40th slice of 5% noise, PD, 7% noise, T2w, the MRI of 7% noise is denoised,
The slice contains more complete human brain edge and detailed information, is denoised with above-mentioned three kinds of algorithms, and index peak letter must be denoised
It makes an uproar more as shown in table 1 than (PSNR) and structural similarity (SSIM) comparison.Wherein T2w, 7% noise image is as shown in figure 3, denoising
Contrast on effect image is as shown in Figure 4.
The different denoising method index comparisons of table 1
Experiment 2: to T2w, the 40th to the 100th slice of the MRI of 7% noise is gone respectively with above-mentioned three kinds of algorithms
It makes an uproar, denoising index PSNR and SSIM comparison is as shown in Figure 5.
Experiment 3: to the T2w of artificial plus noise, the 40th slice is tested, and noise grade is gradually increased to from 3%
15%, interval 2% obtains the denoising index comparison of different denoising methods.As shown in Figure 6
It can be good at realizing image denoising by above-mentioned three groups of description of test inventive algorithms, pass through comparison, it was demonstrated that this
The algorithm of invention can obtain highest PSNR and SSIM, good visual effect, and strong robustness substantially, be applicable in different noise levels
MRI denoising, can clearly retain the edge and detailed information of MRI.
Claims (1)
1. the neighborhood based on card side's unbiased esti-mator shrinks MRI denoising method, this method is making an uproar for this Rician of MRI Lay distribution
Acoustic image includes the following steps:
Step 1 estimates noise criteria difference σ in the background area of MRI:
μ is the mean value for the background area pixels value chosen,
Step 2, then divided by square of noise criteria difference σ, obtains image y to noise image m progress square；
Y=m2/σ2 (2)
Step 3 carries out not normalized steady haar wavelet transform to y, decomposes L layers, obtains high frequency coefficient and low frequency coefficient, high frequency
Coefficient has L*3 subband；
Step 4 is to low frequency coefficient two-sided filter deblurring, to each subband of high frequency coefficient in scheduled threshold search model
Enclose it is interior optimal noise-removed threshold value is determined according to card side's unbiased esti-mator, then with neighborhood contraction method denoise,
Wavelet coefficient after step 5 pair denoising carries out cyclic shift, moves right respectively i, to moving down j, i ∈ [0,2], j ∈
[0,2] carries out inverse wavelet transform, then counter translates
Step 6 by?
Step 7 is to obtainingThe final denoising image being averaging
Card side's unbiased esti-mator of wavelet field, if currently processed small echo high-frequency sub-band coefficient is W, corresponding low frequency scale system
Number is s, and the small echo high-frequency sub-band coefficient after neighborhood is shunk is θ (W), card side's unbiased esti-mator of l layers of denoising small echo high frequency coefficient
Expression formula is expressed as follows through deriving:
Wherein, Kl=2lK, K are freedom degrees, when magnetic resonance tool unicoil is acquired and is imaged, K=2, NlFor small echo high-frequency sub-band
The number of coefficient, T are the operation of matrix transposition,
Optimal noise-removed threshold value is determined according to card side's unbiased esti-mator, and main contents are the accurate meter of the derivative of neighborhood shrinkage method
It calculates,
Neighborhood shrinkage method considers currently pending small echo high-frequency sub-band coefficient wpqCentered on square neighborhood Bpq, BpqFor 3*3's
Neighborhood, give square neighbour coefficient andIf λ is the global threshold of current small echo high-frequency sub-band, w is usednIt indicates
wpq, SnIndicate Spq, then threshold value shrinkage formula can state are as follows:
In formula, θ (wn) be denoising after small echo high-frequency sub-band coefficient, optimal threshold value λ is determined with card side's unbiased esti-matoropt, i.e.,
λopt=argmin CURE (λ), wherein CURE indicates that card side's unbiased esti-mator, window size take 3*3, and card side's unbiased esti-mator needs to count
Calculate θ (wn) single order and second-order differential, by layering derivation steps are as follows:
It enablesThen
G=max (u, 0) is enabled, then
G=f (u)
F (u)=u.*I (u)
F ' (u)=I (u)+I ' (u) .*u
F " (u)=2I ' (u)+I " (u) .*u
Card side's unbiased esti-mator has smooth requirement to denoising function, and g=max (u, 0) must be done smoothly, utilize incomplete βfunction
It does smoothly, if smooth denoising function is g=f (u)=u.*I (u), wherein
In formula, a, b are for controlling smooth degree, in order to guarantee in smooth curve
The heart is symmetrical, and a, b palpus value are identical, a=b=80.
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| Wavelet domain non-linear filtering for MRI denoising;C.Shyam Anand et al.;《Magnetic Resonance Imaging》;20101231;第28卷;摘要，第2.2节倒数第1段，第3节 |
| 一种新的阈值函数的平移不变多小波去噪方法;季桂树;《软件导刊》;20110731;第10卷(第7期);第2.1节，图1 |
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