CN103218795A - Partial K space sequence image reconstruction method based on self-adapted double-dictionary learning - Google Patents

Abstract

The invention discloses a partial K space sequence image reconstruction method based on self-adapted double-dictionary learning, and the method is mainly used for solving the problems of an existing method that the quality of a reconstructed image is more seriously reduced under the condition of sampling under 10 times. The partial K space sequence image reconstruction method comprises the following main steps of: collecting partial K space data and utilizing the correlation between the partial K space data to be integrated into complete K space data; obtaining a training image by the complete K space data; utilizing a KSVD (Kernel Singular Value Decomposition) algorithm to train the training image to obtain dictionaries with high and low resolution ratios; and utilizing a relation between the dictionaries with the high and low resolution ratios to reconstruct the input partial K space data, and carrying out residual error compensation on the reconstructed image to obtain a more accurate reconstruction result. According to the partial K space sequence image reconstruction method disclosed by the invention, the quality of the reconstructed image can be effectively improved under the condition of sampling under 10 times; and the partial K space sequence image reconstruction method can be used for reconstructing MRI (Magnetic Resonance Imaging) sequence images of a plurality of parts.

Description

Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary

Technical field

The invention belongs to technical field of image processing, relate to the method for Medical Image Processing, can be used for the MRI image reconstruction at a plurality of positions.

Background technology

The reconstruct of Partial K spatial image is that propose in order to accelerate the magnetic resonance image (MRI) image taking speed a kind of reduces the problem that the data acquisition amount is come the reconstruct high-definition picture.In order to address this problem, have a lot of classic methods to be suggested:

First kind is the most frequently used zero padding method, and promptly the K spatial data of not gathering is filled up with zero, does the formation method that Fourier inversion obtains image space then, and this formation method can improve image taking speed, and defective is that pseudo-shadow is arranged in the image.

Second kind is the phase correction method, and the phase place in this class methods hypothesis magnetic resonance image (MRI) space is slow variable condition.It estimates phase place with the image of part low frequency K spatial data reconstruct, and is used for phase correction, thereby reaches the purpose of utilizing symmetry to replenish the K spatial data of not gathering.Stark, the POCS method that H. proposes is exactly a modal method in these class methods.But because the condition that the magnetic resonance image (MRI) phase place slowly changes usually is difficult to satisfy in the entire image space, cause the phase estimation error big, cause bigger reconstructed error, so that up to the present can't in clinical medicine, use.

The third is the signal estimation technique, and this method utilization signal estimation theory is utilized the interpolation of Partial K spatial data, spreaded to method such as multiple-objection optimization outward and obtain the K spatial data of not gathering.M.Funderer has proposed the method for image maximum likelihood in 1989, E.M.Haacke is the typical method of these class methods at the constrained procedure that propose the same year, and this class methods imaging effect is far inferior to method for correcting phase.

The 4th kind is the singular spectrum modelling, the thought of these class methods is based on the fact that any signal can be represented with the weighted sum of singular function, set up new image expression model,, go out complete K space by model and parameter reconstruct then by Partial K spatial data extraction model parameter.This method in most cases is better than the phase correction method and the signal estimation technique.

The 5th kind is the method for compressed sensing, and this method is utilized small echo, finite difference, and dictionary study etc. is carried out rarefaction representation to reconstructed image, and the effect of these class methods in most cases all is better than additive method.

Above-mentioned Partial K Space Reconstruction method all needs sampling rate to reach more than 30% usually, could obtain reconstruct effect preferably.But sampling rate is high more, and required acquisition time is long more, will be trapped in for a long time in the Image-forming instrument by imaging person, owing to will be made image produce motion blur by imaging person's motion.Yet, further reduce sampling rate and can cause reconstructed image to produce pseudo-shadow and the low problem of image resolution ratio.

Summary of the invention

The objective of the invention is to deficiency, propose a kind of Partial K spatial sequence image reconstructing method,, improve the quality of reconstructed image to reduce data sampling rate based on the study of self-adaptation doubledictionary at above-mentioned prior art.

For achieving the above object, the present invention includes following steps:

(1) gathers N width of cloth Partial K spatial data, with synthetic n the complete K spatial data Q of this N width of cloth Partial K spatial data _i, i=1,2 ..., n; To Q _iCarry out 10 times of down-samplings, obtain corresponding Partial K spatial data P _iTo Q _iMake Fourier inversion, obtain high-definition picture H _i, to P _iMake Fourier inversion, obtain low-resolution image L _i, this n to high-definition picture H _iWith low-resolution image L _iAs training image;

(2) import high resolving power training image H respectively _iWith low resolution training image L _i, and adopt nonoverlapping mode that every width of cloth training image is got 4 * 4 fritter, obtain initial high resolution dictionary H and initial low resolution dictionary L;

(3) utilize the KSVD algorithm that initial high resolution dictionary H and initial low resolution dictionary L are trained, obtain new high resolving power dictionary D _hWith new low resolution dictionary D _l, and high-definition picture H _iSparse factor alpha _HiWith low-resolution image L _iSparse factor alpha _Li

(4) the Partial K spatial data P of reconstruct is treated in input _t, to this Partial K spatial data P _tAdopt the zero padding method to handle, obtain initial reconstitution image L _t,

(5) utilize low resolution dictionary D _lWith initial reconstitution image L _t, find the solution initial reconstitution image L _tSparse factor alpha _l

(6) ask initial reconstitution image L respectively _tWith n width of cloth low resolution training image L _iError:

Obtain initial reconstitution image L _tWith the j width of cloth training image L in the n width of cloth low resolution training image _jLeast error: $e{r}_j=\underset{i=1}{\overset{n}{\min }}\left\{e{r}_i\right\};$

(7) judge least error er _jWhether less than preset threshold σ=0.1, if error e r _jLess than threshold value σ, obtain the high-definition picture H that treats reconstruct _t' sparse factor alpha _hIf error e r _jGreater than threshold value, return step (1), gather N width of cloth Partial K spatial data again, upgrade dictionary;

(8) utilize high resolving power dictionary D _hWith the high-definition picture H that treats reconstruct _t' sparse factor alpha _h, try to achieve high-definition picture: H _t'=D _h* α _hAgain to changing high-definition picture H _t' carry out residual compensation, obtain final reconstructed image H _t

The present invention has the following advantages compared with prior art:

1. the present invention utilizes the correlativity between the Partial K spatial sequence data to synthesize several complete K spatial datas, obtain training image by these complete K spatial datas, and utilize these training images to train dictionary, thereby the quantity of information that dictionary comprises is abundanter, can reconstruct the detailed information of image preferably;

2. the present invention makes the adaptivity of dictionary stronger because variation between sequence image is upgraded dictionary when big, has improved the robustness of reconstruct, promptly all can obtain reconstruct effect preferably to 1800 width of cloth sequence datas;

Simulation result shows that the present invention can just can carry out high-quality reconstruct to the MRI image under the condition of 10 times of down-samplings, reduced data sampling rate, has shortened data acquisition time.

Description of drawings

Fig. 1 is a general flow chart of the present invention;

Fig. 2 is with the reconstruct design sketch of the present invention to the 100th width of cloth chest test pattern;

Fig. 3 is with the reconstruct design sketch of the present invention to the 70th width of cloth belly test pattern.

Specific implementation method

With reference to accompanying drawing 1, concrete steps of the present invention comprise as follows:

Step 1. is synthesized complete K spatial data, obtains training image

1a) gather N width of cloth Partial K spatial data, with synthetic n the complete K spatial data Q of this N width of cloth Partial K spatial data _i, i=1,2 ..., n, the method for generated data has synthetic method based on Pixel-level, based on the synthetic method of feature level with based on the synthetic method of decision level etc., and this example adopts but is not limited to synthetic method based on Pixel-level, and its building-up process is as follows:

With the synthetic width of cloth K spatial data of N/n width of cloth Partial K spatial data, be standard with first width of cloth Partial K spatial data of this N/n width of cloth Partial K spatial data;

What collect in second width of cloth Partial K space, and the data that first width of cloth Partial K space does not collect are added on first width of cloth Partial K space;

What collect in the 3rd width of cloth Partial K space, and the data that preceding two width of cloth Partial K spaces all do not collect are added on first width of cloth Partial K space, by that analogy, and synthetic n complete K spatial data Q _i

1b) to above-mentioned spatial data Q _iCarry out 10 times of down-samplings, obtain corresponding Partial K spatial data P _iTo Q _iMake Fourier inversion, obtain high-definition picture H _i, to P _iMake Fourier inversion, obtain low-resolution image L _i, this n to high-definition picture H _iWith low-resolution image L _iAs training image.

Step 2. pair training image carries out pre-service

Import high resolving power training image H respectively _iWith low resolution training image L _i, and adopt nonoverlapping mode that every width of cloth training image is got 4 * 4 fritter, obtain initial high resolution dictionary H and initial low resolution dictionary L.

Step 3. training high-resolution and low-resolution dictionary

Initial high resolution dictionary H and initial low resolution dictionary L are trained, obtain new high resolving power dictionary D _hWith new low resolution dictionary D _l, and high-definition picture H _iSparse factor alpha _HiWith low-resolution image L _iSparse factor alpha _Li, the method for training dictionary mainly contains two kinds, is respectively principal component analysis (PCA) PCA and K singular value decomposition method KSVD, and what this example used is that the KSVD algorithm is trained, and its training process is as follows:

3a) to total optimization formula of KSVD algorithm: $\min \left\{{\left|\right|Y-\mathrm{DX}\left|\right|}_F^2\right\}\mathrm{Subject\; to}\∀l,{\left|\right|X_l\left|\right|}_0\≤T_0,$ Be out of shape, be about to optimization formula wherein

Be deformed into:

${\left|\right|Y-\mathrm{DX}\left|\right|}_F^2={\left|\right|Y-\underset{m=1}{\overset{k}{\mathrm{\Σ}}}{d}_m{x}_T^m\left|\right|}_F^2={\left|\right|(Y-\underset{m\≠k}{\mathrm{\Σ}}{d}_m{x}_T^m)-d_k{x}_T^k\left|\right|}_F^2={\left|\right|E_k-d_k{x}_T^k\left|\right|}_F^2,$

Wherein, Y is the initial dictionary of input, and D is a target training dictionary, and X is the Sparse Decomposition matrix,

Be any l row, ‖ X _l‖ ₀Be X _l0 norm,

For finding the solution 2 norms of Y-DX, T ₀Be the degree of rarefication control coefrficient; d _mBe the m row atom of D,

For the m of X is capable, K is total columns of D, d _kBe the k row atom of target training dictionary D,

For the k of X is capable, E _kFor not using the k row atom d of D _kCarry out the error matrix that the signal Sparse Decomposition is produced;

3b) to the optimization formula after the distortion

Multiply by matrix Ω _k=P*| ω _k|, obtain the target decomposition formula ${\left|\right|E_k{\mathrm{\Ω}}_k-d_k{x}_T^k{\mathrm{\Ω}}_k\left|\right|}_F^2={\left|\right|E_k^R-d_k{x}_R^k\left|\right|}_F^2,$

Wherein

Ω _kSize be P*| ω _k|, P is the columns of the initial dictionary Y of input,

| ω _k| be ω _kThe mould value, and Ω _kAt (ω _k(m), m) locating is 1, and other place is 0 entirely, wherein 1≤m≤| ω _k|, ω _k(m) be ω _kThe m number;

3c) to the target decomposition formula

In error matrix

Carrying out decomposition of singular matrix obtains

Wherein U is a left singular matrix, V ^TBe right singular matrix, Φ is a singular value matrix;

3d) get k=1 successively, 2 ..., K is listed as the more k row atom of fresh target train word allusion quotation D with first of left singular matrix U, tries to achieve the dictionary D ' after the renewal, obtains new high resolving power dictionary D _hWith new low resolution dictionary D _l

3e) utilize the initial dictionary Y of input and the dictionary D ' after the renewal, try to achieve Sparse Decomposition matrix X ', obtain high-definition picture H _iSparse factor alpha _HiWith low-resolution image L _iSparse factor alpha _Li

The Partial K spatial data of reconstruct is treated in step 4. pre-service

4a) the Partial K spatial data P of reconstruct is treated in input _t, to this Partial K spatial data P _tCarry out pre-service, obtain initial reconstitution image L _t,

Pretreated method can be used the zero padding method, the phase correction method, and the signal estimation technique etc., this example uses the zero padding method to this Partial K spatial data P _tIn after the data padding of not gathering, carry out Fourier inversion again, obtain initial reconstitution image L _t

4b) utilize low resolution dictionary D _lWith initial reconstitution image L _t, find the solution initial reconstitution image L _tSparse factor alpha _l, find the solution sparse factor alpha _lCan use matching pursuit algorithm, basic tracing algorithm, orthogonal matching pursuit algorithm etc., this example uses the orthogonal matching pursuit algorithm, tries to achieve initial reconstitution image L _tSparse factor alpha _l, its solution formula is: L _t=D _lα _l

Step 5. is found the solution the sparse coefficient of high-definition picture

5a) ask initial reconstitution image L respectively _tWith n width of cloth low resolution training image L _iError:

$e{r}_i=\frac{{\left|\right|L_t-L_i\left|\right|}_2}{{\left|\right|L_t\left|\right|}_2}$

Obtain initial reconstitution image L _tWith the j width of cloth training image L in the n width of cloth low resolution training image _jLeast error: $e{r}_j=\underset{i=1}{\overset{n}{\min }}\left\{e{r}_i\right\};$

5b) judge least error er _jWhether less than preset threshold σ=0.1,

If error e r _jGreater than threshold value σ, then return step 1, gather N width of cloth Partial K spatial data again, upgrade dictionary;

If error e r _jLess than threshold value σ, obtain the high-definition picture H that treats reconstruct _t' sparse factor alpha _h, solution procedure is:

5b1) ask low resolution difference matrix: Δ l=α _l-α _Lj, wherein, α _lBe initial reconstitution image L _tSparse coefficient, α _LjBe low resolution training image L _jSparse coefficient;

5b2) obtain high resolving power difference matrix Δ h by low resolution difference matrix Δ l:

Make that Δ h is that an element is zero matrix entirely, matrix size equates with Δ l, obtains the average a of all non-vanishing elements among the Δ l;

5b3) find out high resolving power training image H _jSparse factor alpha _HjIn the non-vanishing position of all elements, make that the element on the same position equals a among the Δ h;

5b4) utilize high resolving power difference matrix Δ h and high resolving power training image H _jSparse factor alpha _Hj, try to achieve and treat reconstruct high-definition picture H _t' sparse coefficient: α _h=α _Hj+ Δ h.

Step 6. reconstruct high-definition picture

6a) utilize high resolving power dictionary D _hWith the high-definition picture H that treats reconstruct _t' sparse factor alpha _h, try to achieve high-definition picture: H _t'=D _h* α _h

6b) to high-definition picture H _t' carry out residual compensation, the method for residual compensation has inverse iteration residual compensation method, and based on residual compensation method of localized mass etc., this example is based on the residual compensation method of entire image, and detailed process is as follows:

6b1) carry out Fourier transform, 10 times of down-samplings, inversefouriertransform successively, obtain low-resolution image L _t';

6b2) try to achieve low-resolution image L _t' with initial reconstitution image L _tResidual error: Δ=L _t-L _t';

6b3) according to high-definition picture H _t' and residual delta, try to achieve final reconstructed image H _t=H _t'+Δ.

Effect of the present invention can further specify by following experiment:

1) experiment condition

1800 width of cloth chest MRI test patterns are adopted in this experiment respectively, and size is 192 * 160, and 1800 width of cloth belly MRI test patterns, and size is 192 * 176 as experimental data.

2) experiment content

Utilize zero padding method, PBDW algorithm, TVCMRI algorithm and the present invention respectively, the test pattern of importing be reconstructed:

At first, 1800 width of cloth chest images are reconstructed, wherein, to the reconstruction result of the 100th width of cloth chest image as shown in Figure 2, wherein Fig. 2 (a) is that the 100th width of cloth chest test pattern, Fig. 2 (b) are the reconstruction result of TVCMRI, Fig. 2 (f) of the present invention reconstruction result for the reconstruction result of zero padding method, Fig. 2 (d) for the reconstruction result of PBDW, Fig. 2 (e) for the 100th width of cloth Partial K spatial data image, Fig. 2 (c) of input;

Secondly, 1800 width of cloth abdomen images are reconstructed, wherein, to the reconstruction result of the 70th width of cloth abdomen images as shown in Figure 3, wherein Fig. 3 (a) is that the 70th width of cloth belly test pattern, Fig. 3 (b) are the reconstruction result of TVCMRI, Fig. 3 (f) of the present invention reconstruction result for the reconstruction result of zero padding method, Fig. 3 (d) for the reconstruction result of PBDW, Fig. 3 (e) for the 70th width of cloth Partial K spatial data image, Fig. 3 (c) of input;

3) interpretation

As can be seen from Figures 2 and 3, the present invention is better than other method on the visual effect of reconstructed image, it is relatively good that the detailed information of image all keeps, and for the input picture such as the chest image at each position, abdomen images can obtain good reconstruct effect.

Claims (7)

1. the Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary comprises the steps:

(1) gathers N width of cloth Partial K spatial data, with synthetic n the complete K spatial data Q of this N width of cloth Partial K spatial data _i,

To Q _iCarry out 10 times of down-samplings, obtain corresponding Partial K spatial data P _iTo Q _iMake Fourier inversion, obtain high-definition picture H _i, to P _iMake Fourier inversion, obtain low-resolution image L _i, this n to high-definition picture H _iWith low-resolution image L _iAs training image;

(2) import high resolving power training image H respectively _iWith low resolution training image L _i, and adopt nonoverlapping mode that every width of cloth training image is got 4 * 4 fritter, obtain initial high resolution dictionary H and initial low resolution dictionary L;

(3) utilize the KSVD algorithm that initial high resolution dictionary H and initial low resolution dictionary L are trained, obtain new high resolving power dictionary D _hWith new low resolution dictionary D _l, and high-definition picture H _iSparse factor alpha _HiWith low-resolution image L _iSparse factor alpha _Li

(4) the Partial K spatial data P of reconstruct is treated in input _t, to this Partial K spatial data P _tAdopt the zero padding method to handle, obtain initial reconstitution image L _t,

(5) utilize low resolution dictionary D _lWith initial reconstitution image L _t, find the solution initial reconstitution image L _tSparse factor alpha _l

(6) ask initial reconstitution image L respectively _tWith n width of cloth low resolution training image L _iError:

Obtain initial reconstitution image L _tWith the j width of cloth training image L in the n width of cloth low resolution training image _jLeast error:

(7) judge least error er _jWhether less than preset threshold σ=0.1, if error e r _jLess than threshold value σ, obtain the high-definition picture for the treatment of reconstruct

Sparse factor alpha _hIf error e r _jGreater than threshold value, return step (1), gather N width of cloth Partial K spatial data again, upgrade dictionary;

(8) utilize high resolving power dictionary D _hWith the high-definition picture for the treatment of reconstruct

Sparse factor alpha _h, try to achieve high-definition picture:

Again to changing high-definition picture

Carry out residual compensation, obtain final reconstructed image H _t

2. the Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary according to claim 1, wherein step (1) is described with synthetic n the complete K spatial data Q of the N width of cloth Partial K spatial data of gathering _i, i=1,2 ..., n, carry out as follows:

2a) with the synthetic width of cloth K spatial data of N/n width of cloth Partial K spatial data, be standard with first width of cloth Partial K spatial data of this N/n width of cloth Partial K spatial data;

2b) collecting in second width of cloth Partial K space, and the data that first width of cloth Partial K space does not collect are added on first width of cloth Partial K space;

2c) collecting in the 3rd width of cloth Partial K space, and data that preceding two width of cloth Partial K spaces all do not collect are added on first width of cloth Partial K space, by that analogy, and synthetic n complete K spatial data Q _i

3. the Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary according to claim 1, wherein step (3) is described trains initial high resolution dictionary H and initial low resolution dictionary L, carries out as follows:

3a) to KSVD optimization Algorithm formula: Be out of shape, be about to wherein

Be expressed as:

Wherein, Y is the initial dictionary of input, and D is a target training dictionary, and X is the Sparse Decomposition matrix,

Be any l row, ‖ X _L0‖ is X _l0 norm,

For finding the solution 2 norms of Y-DX, T ₀Be the degree of rarefication control coefrficient; d _mBe the m row atom of D,

For the m of X is capable, K is total columns of D, d _kBe the k row atom of target training dictionary D, For the k of X is capable, E _kFor not using the k row atom d of D _kCarry out the error matrix that the signal Sparse Decomposition is produced;

3b) to the formula after the distortion

Multiply by matrix Ω _k, obtain the target decomposition formula

Wherein

Ω _kSize be P*| ω _k|, P is the columns of the initial dictionary Y of input, ω _k=l|1≤l≤K,

| ω _k| be ω _kThe mould value, and Ω _kAt (ω _k(m), m) locating is 1, and other place is 0 entirely, wherein 1≤m≤| ω _k|, ω _k(m) be ω _kThe m number;

3c) to the target decomposition formula

In error matrix Carrying out decomposition of singular matrix obtains

Wherein U is a left singular matrix, V ^TBe right singular matrix, Φ is a singular value matrix;

3d) get k=1 successively, 2 ..., K is listed as the more k row atom of fresh target train word allusion quotation D with first of left singular matrix U, tries to achieve the dictionary D ' after the renewal, obtains new high resolving power dictionary D _hWith new low resolution dictionary D _l

3e) utilize the initial dictionary Y of input and the dictionary D ' after the renewal, try to achieve Sparse Decomposition matrix X ', obtain high-definition picture H _iSparse factor alpha _HiWith low-resolution image L _iSparse factor alpha _Li

4. the Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary according to claim 1, wherein step (4) is described to Partial K spatial data P _tAdopting the zero padding method to handle, is to after the data padding of not gathering, and carries out Fourier inversion again, obtains reconstructed image.

5. the Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary according to claim 1, the wherein described low resolution dictionary D that utilizes of step (5) _lWith initial reconstitution image L _t, find the solution initial reconstitution image L _tSparse factor alpha _l, its solution formula is: L _t=D _lα _l

6. the Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary according to claim 1, the wherein described high-definition picture H that treats reconstruct that obtains of step (7) _t' sparse factor alpha _h, carry out as follows:

6a) ask low resolution difference matrix: Δ l=α _l-α _Lj, wherein, α _lBe initial reconstitution image L _tSparse coefficient, α _LjBe low resolution training image L _jSparse coefficient;

6b) obtain high resolving power difference matrix Δ h by low resolution difference matrix Δ l:

Make that Δ h is that an element is zero matrix entirely, matrix size equates with Δ l, obtains the average a of all non-vanishing elements among the Δ l;

Find out high resolving power training image H _jSparse factor alpha _HjIn the non-vanishing position of all elements, make that the element on the same position equals a among the Δ h;

6c) utilize high resolving power difference matrix Δ h and high resolving power training image H _jSparse factor alpha _Hj, try to achieve and treat reconstruct high-definition picture H _t' sparse coefficient: α _h=α _Hj+ Δ h.

7. according to the described Partial K spatial sequence image reconstructing method based on the study of self-adaptation doubledictionary of claim 1, wherein step (8) is described to high-definition picture H _t' carry out residual compensation, carry out as follows:

7a) to high-definition picture H _t' carry out Fourier transform, 10 times of down-samplings, inversefouriertransform successively, obtain low-resolution image L _t';

7b) try to achieve low-resolution image L _t' with initial reconstitution image L _tResidual error: Δ=L _t-L _t';

7c) try to achieve final reconstructed image H _t=H _t'+Δ.

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