CN105654528B - Compressed sensing based multipotency X-ray method for separate imaging - Google Patents

Compressed sensing based multipotency X-ray method for separate imaging Download PDF

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CN105654528B
CN105654528B CN201610007762.3A CN201610007762A CN105654528B CN 105654528 B CN105654528 B CN 105654528B CN 201610007762 A CN201610007762 A CN 201610007762A CN 105654528 B CN105654528 B CN 105654528B
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CN105654528A (en
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喻春雨
费彬
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Nanjing Post and Telecommunication University
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
    • G—PHYSICS
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract

The invention discloses compressed sensing based multi-energy X-ray image separation methods, belong to the technical field of medical image image procossing.The present invention perceives human body X ray sequence picture signal according to compressive sensing theory, establish the excessively complete base independent component analysis model based on image perception signal, it is standard independent component analysis model by excessively complete base independent component analysis model conversation, the medical image echo signal of estimation standard independent component analysis model, in conjunction with compressive sensing theory reconstruction signal.Compression time of the present invention is short, reconstitution time is short, reconstructed image quality is high, and calculation amount is reduced while guaranteeing reconstructed image quality and optimizes independent composition analysis algorithm complexity.

Description

Compressed sensing based multipotency X-ray method for separate imaging
Technical field
The invention discloses the multipotency X-rays based on compressed sensing (Compressive Sensing, CS) to be separated into image space Method belongs to the technical field of image processing of medical image.
Background technique
Aiming at the problem that, stereovision big Traditional x-ray picture noise is poor and organ-tissue is overlapped, propose to utilize multi-power spectrum X Ray image characteristic combination independent component analysis (Independent Component Analysis, ICA) carries out target separation. The thickness matrix that each pixel in image corresponds to target is isolated according to target composition X ray attenuation characteristics difference each in image； The convergence number and amplitude size for adjusting ICA algorithm obtain convergent matrix, reconstruct target object.It is this tradition ICA algorithm into When row is rebuild, algorithm operation quantity it is heavy and it is unsuitable chose complete dictionary as sparse matrix, and utilization is adaptive excessively complete Dictionary is the trend for reducing image-processing operations amount, this belongs to CS technology scope.CS is a kind of new signal processing theory, by D.Donoho, E.Candes and scientist T.Tao of Chinese origin et al. are proposed, have just greatly attracted correlative study from being born certainly The concern of personnel.
Summary of the invention
The technical problem to be solved by the present invention is to be directed to the deficiency of above-mentioned background technique, the multipotency X based on CS is provided and is penetrated Line method for separate imaging, in CS theoretical basis, by improved ICA algorithm be nested in signal sparseness measuring and signal reconstruction it Between, it is ensured that the adaptivity of rarefaction and the quality of separate picture, when improving using traditional IC A progress X-ray separate imaging Long operational time and the big defect of memory occupancy volume.
The present invention adopts the following technical scheme that for achieving the above object：
CS is applied in ICA image Separation Research by the present invention, and algorithm is by the perception of original image signal, the signal based on ICA Separation and echo signal reconstruct three parts are constituted, and specific implementation sequence is：Obtain the X-ray sequence image of different ray energies s1,s2,...,sn, as original image signal, indicated with matrix S；It uses perception matrix (i.e. sparse matrix ψ and calculation matrix φ) Original image signal is handled, corresponding image perception signal x is obtained01′,x02′,...,x0n', with matrix X0' indicate；By standard ICA model perception signal X made complete ICA model conversion standard ICA model X by regression algorithm；Using FastICA to sense Know that signal is separated, obtains radioscopic image echo signal y1,y2,...,yn, indicated with Y；Using orthogonal matching pursuit algorithm Radioscopic image echo signal Y is reconstructed, reconstructed image signal o is obtained1,o2,...,on。
Further, standard ICA model is：
Wherein, X is the perceptual signal of standard ICA model, X'0It is original X-rays image sequence signal by perception matrix Perceive obtained perceptual signal, X'mFor non-perceptual signal, the dimension m of perceptual signal believes less than original X-rays image sequence Number dimension n, S' be sparse component of the original X-rays image sequence signal in sparse basis, A'0For the target of perceptual signal Thickness matrix, A'mFor the target thickness matrix of non-perceptual signal.
It further, is with the following method standard by excessively complete base ICA model conversation in the separate picture method ICA model：
Perceptual signal part in abstract image perceptual signal indicates non-perceptual signal portion in conjunction with European squared-distance Point；
According to linear regression analysis and combination, perceptual signal model obtains the expectation of non-perceptual signal, will not perceive letter Number expectation substituted into complete base ICA model and obtain standard ICA model.
Further, it in the separate picture method, limit theorem and is asked using quasi- orthogonal FastICA algorithm according in Solution standard ICA model, isolated source signal perceptual signal estimated value y1,y2,...,yn。
Further, in the method for separate imaging, the specific method of step D is：
To the isolated source signal perceptual signal estimated value that step C is obtained, original X is acquired using orthogonal matching pursuit algorithm Ray image series signal sparse component in sparse basis approaches value, then obtains original X-rays image sequence by the value of approaching The reconstruction value of column signal to get to separation target image o1,o2,...,on。
The present invention by adopting the above technical scheme, has the advantages that：
(1) for multi-energy X-ray image noise is big, contrast is low and human organ mutual superimposed the characteristics of not being easily distinguishable, Based on CS technology, nested " the multipotency X-ray method for separate imaging based on CS " for improving ICA between signal is perceived and reconstructed, Optimize ICA algorithm while guaranteeing reconstructed image quality, reduce calculation amount；
It (2) is standard ICA model by excessively complete ICA model conversation, prominent area-of-interest and marginal information improve image Visual effect, obtain image that is intuitive, clear and being suitable for medical analysis.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the multipotency X-ray method for separate imaging of compressed sensing.
Fig. 2 (a), Fig. 2 (b), Fig. 2 (c) are the X ray picture of three kinds of energy respectively.
It is sparse basis that Fig. 3 (a), Fig. 3 (b), Fig. 3 (c) choose DCT dictionary, DWT dictionary and the excessively complete dictionary of K-SVD respectively When comparison in terms of compression time, reconstitution time, reconstructed image quality.
Fig. 4 (a) to Fig. 4 (c), Fig. 4 (g) to Fig. 4 (i) be respectively previous work " the X-ray medical image mesh based on ICA Mark extracts " gained reconstructs subgraph and the application work gained reconstructs subgraph；Fig. 4 (d) to Fig. 4 (f), Fig. 4 (j) are to Fig. 4 (l) The respectively edge extracting figure of previous work and the present invention 3 subgraphs of reconstruct.
Specific embodiment
The technical solution of invention is described in detail with reference to the accompanying drawing.
CS is applied in ICA image Separation Research in this patent, algorithm is by the perception of source images signal, the letter based on ICA Number separation and echo signal reconstruct three parts constitute, process and realize steps are as follows：
Step1:Obtain original sequence X0, it passes through coefficient matrices A by source signal S0Linear combination forms, and indicates such as Under：
X0=A0S (1)
Step2:To original sequence X0Signal perception processing is carried out, at this time perceptual signal X'0Variable number m believes less than source (base vector number n), base vector is for perceptual signal X' by number S scalar number n0It was complete (Overcomplete).
X'0=φ X0=φ (A0S)=φ A0(ψTS')=A'0S' (2)
In formula (2), φ is calculation matrix, and ψ is the sparse basis of source signal S, and S' is sparse point of source signal S in sparse basis Amount；
Step3：By perceptual signal X'0Acquire X'm, i.e., made complete ICA model conversation standard ICA mould by returning ICA Type.
In formula (3), X'mContaining n-m variable, with X'0M variable collectively constitute n variable.Wherein, X'mIt can be by such as Lower conditional expectation acquires：
In formula (4), p (S') is the probability density function of S'.The X' assuming that integral that function g () is formula (4) is recorded a demeritm。
Step4:Standard ICA model is used to formula (3), the signal source sense separated with quasi- orthogonal FastICA algorithm Know signal estimated value y1,y2,...,yn。
Step5:To separation estimated value y1,y2,...,ynPass through orthogonal matching pursuit algorithm (Orthogonal Matching Pursuit, OMP) value of approaching of S' is acquired, and then the reconstruction value of source signal S is obtained by its sparse basis, that is, separate target image o1,o2,...,on。
Algorithm performance comparison
Using the simulation radioscopic image under three kinds of voltages as original image in conjunction with shown in Fig. 2 (a), Fig. 2 (b) and Fig. 2 (c), benefit With this application involves CS be that processing method successively carries out signal compression to it, separates and reconstruct in conjunction with ICA.
Choosing DCT dictionary, DWT dictionary and the excessively complete dictionary of K-SVD respectively is sparse basis, and is equipped with gaussian random measurement square Battle array, FastICA separation algorithm, OMP restructing algorithm analyze different sparse basises in compression time, reconstitution time, reconstructed image quality On performance.Fig. 3 (a) provides relationship between the compression algorithm time and sampling precision of three kinds of sparse basises, as seen from the figure, when compression Between with sampling precision increase and increase；When sampling precision is identical, compression time needed for the algorithm using the excessively complete dictionary of K-SVD It is most short.Fig. 3 (b) provides relationship between the algorithm reconstitution time and sampling precision of three kinds of sparse basises, as seen from the figure, reconstitution time with Sampling precision increase and increase；When sampling precision is identical, reconstitution time needed for the algorithm using the excessively complete dictionary of K-SVD is most It is short.Fig. 3 (c) provide the algorithm reconstructed image of three kinds of sparse basises peak value signal-to-noise ratio (Peak Signal to Noise Ratio, PSNR) the relationship between sampling precision, as seen from the figure, slightly higher using K-SVD sparse basis algorithm, DWT sparse basis is taken second place；[40, 70] within the scope of sampling precision, the PSNR value difference of reconstructed image is different smaller.It to sum up analyzes, the application is carried out using K-SVD sparse basis Picture signal can more preferably be restored after signal perception.
In previous work " the X-ray medical image Objective extraction based on ICA ", it is first depending on each target composition in image Characteristic isolates the thickness matrix of corresponding target, then adjustment convergence number and amplitude size, obtains convergent matrix with ICA Reconstruct target object.Though this method can separate aliasing target, calculation amount can be substantially reduced by this paper algorithm.To sum up Analysis, the application take the excessively complete sparse dictionary of K-SVD as sparse basis, will be preliminary using random gaussian matrix as calculation matrix Picture signal that treated is separated by excessively complete ICA, and is reconstructed with OMP, and the obtained effect of previous work is compared Fruit improves as follows.
If Fig. 4 (a) to Fig. 4 (c), Fig. 4 (g) to Fig. 4 (i) are respectively reconstruct subgraph obtained by early period and the application work institute Subgraph must be reconstructed, it is seen that gained reconstruct subgraph visual effect is more preferable herein；Further to compare visual effect, Fig. 4 (d) is extremely Fig. 4 (f), Fig. 4 (j) provide reconstructed image early period to Fig. 4 (l) respectively and the application reconstructs the edge extracting figure of 3 subgraphs, by The edge lines for reconstructing subgraph known to comparison herein are apparent, coherent, illustrate that details is richer.
In addition, the runing time in algorithm that works to previous work and herein, memory occupation rate, reconstructed image gradient, It is compared in terms of PSNR and comentropy.Study surface：Compared with previous work, X-ray is carried out based on ICA through CS is improved Image object separation algorithm runing time reduces 46.14s (23.3%), and memory occupation rate reduces by 75%, reconstructed image peak value letter It makes an uproar and improves 2.665dB than (Peak Signal to Noise Ratio, PSNR), edge gradient improves 0.001, and comentropy improves 0.09。

Claims (4)

1. compressed sensing based multipotency X-ray method for separate imaging, which is characterized in that include the following steps：
A, original X-rays image sequence signal is obtained, according to compressive sensing theory perceptual image signal：First with excessively complete word Allusion quotation carries out LS-SVM sparseness to original X-rays image sequence signal, then completes signal to rarefaction signal using calculation matrix Perception；
It B, is standard ICA model by excessively complete base ICA model conversation by regressing calculation by perceptual signal：Abstract image perception letter Perceptual signal part in number indicates non-perceptual signal part in conjunction with European squared-distance, simultaneously according to linear regression analysis The expectation of non-perceptual signal is obtained in conjunction with perceptual signal model, the expectation of non-perceptual signal was substituted into complete base ICA model Obtain standard ICA model；
C, the standard ICA model according to step B acquires separation signal；
D, signal reconstruction is separated described in step C in conjunction with compressive sensing theory to obtain separation target image.
2. compressed sensing based multipotency X-ray method for separate imaging according to claim 1, which is characterized in that step B Described in standard ICA model be：
Wherein, X is the perceptual signal of standard ICA model, X'0It is original X-rays image sequence signals by perceiving matrix The perceptual signal arrived, X'mFor non-perceptual signal, the dimension m of perceptual signal is less than the dimension of original X-rays image sequence signal Number n, S' are sparse component of the original X-rays image sequence signal in sparse basis, A'0For the target thickness square of perceptual signal Battle array, A'mFor the target thickness matrix of non-perceptual signal.
3. compressed sensing based multipotency X-ray method for separate imaging according to claim 1, which is characterized in that step C Specific method be：Limit theorem and the quasi- orthogonal FastICA algorithm solution standard ICA model of utilization, are separated according in Source signal perceptual signal estimated value y1,y2,...,yn。
4. special according to claim 1 to compressed sensing based multipotency X-ray method for separate imaging described in any one of 3 Sign is that the specific method of step D is：
To the isolated source signal perceptual signal estimated value that step C is obtained, original X-rays are acquired using orthogonal matching pursuit algorithm Image sequence signal sparse component in sparse basis approaches value, then by the value of approaching obtains original X-rays image sequence letter Number reconstruction value to get to separation target image o1,o2,...,on。
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