CN104867168B - Compressed sensing computed tomography images method for reconstructing based on p norms - Google Patents
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Abstract
The invention discloses a kind of compressed sensing computed tomography images method for reconstructing based on P norms refers specifically to a kind of CT image algebra iterative reconstruction approach that incomplete projections are carried out with image total variance Lp norm minimums.This method mainly comprises the following steps：(1) CT system imaging parameters and scanning system data for projection are obtained；(2) initial projection data mainly carry out sliding-model control and filtering noise reduction process to data for projection including the use of wavelet transformation base, solve projection matrix by weighting and carry out assignment x to initial pictures x(0)=0；(3) algebraically iterative approximation is carried out to data for projection, doing total variance Lp norm minimums to the image after each iteration using gradient descent method adjusts, and judges whether it meets the condition of convergence.If satisfied, then reconstruction image is preserved and is exported；If not satisfied, then continuing iteration using the adjustment image of epicycle iteration as iterative initial value.
Description
Technical field
The present invention relates to the image processing fields of medical image, more particularly to computed tomography (Computed
Tomography, CT), in particular to a kind of compressed sensing CT image rebuilding methods based on P norms, this method may be implemented by
Incomplete scan data rebuilds the high CT images of high s/n ratio, clarity.It is big that reconstruction image aliasing artefacts, noise can be improved
Problem, to reduce the X-ray radiation time, shorten image reconstruction times.
Background technology
Computed tomography is a kind of digital imaging technology that computer technology and radioactivity detection technology are combined.Always
It is widely used in industrial detection and medical diagnosis.High quality CT images are pursued to generally require for a long time to put testee
It sets under x-ray bombardment, to damage testee.
Radon transformation that mathematician J.Radon is proposed is inversely transformed into CT imagings and has established solid Fundamentals of Mathematics.Parsing
It is CT figures to rebuild (Analytic Reconstruction, AR) and iterative approximation (Iterative Reconstruction, IR)
As the two kinds of basic skills rebuild.Filtered back projection (Filtered Back Projection, FBP) is the common of analytic reconstruction
Algorithm needs the comprehensive scanning to being detected within the scope of 180 ° of human body progress, this will be so that object to be detected exposure for a long time
Under X-ray.Algebraic reconstruction algorithm (Algebraic Reconstruction Technique, ART) is the master of iterative approximation
Algorithm is wanted, algebraically iterative reconstruction algorithm is higher to noise sensitivity, and the amendment image of generation, which will produce, obscures ghost image.But both
When traditional reconstruction algorithm rebuilds incomplete projections, operand needed for algorithm for reconstructing can be increased, cannot be met existing
Demand.And the sample rate of data for projection can have large effect to the details of noisiness, image that reconstruction image includes, utilize
A small amount of data for projection is reconstructed to be of great importance without the CT images for obscuring ghost image.
Compressed sensing (Compressive Sensing, CS) theory is by Terence Tao, Candes and Donoho
Equal propositions.It is realized far below to the direct sampling of compressed data, shortening signal sampling under Nyquist sampling frequency
Time reduces calculation amount, greatly reduces signal processing cost.It can avoid above-mentioned traditional reconstruction algorithm disadvantage.Compression sense
The basic thought known is：Compression sampling, which merges, to carry out, and is projected using the non adaptive of signal to restore signal structure.Compression sense
Know to include mainly sparse signal representation, observing matrix design and signal reconstruction.It is widely used to imaging of medical, using number at present
The multiple fields such as, wireless communication, optics/remotely sensed image.
Image reconstruction research is carried out to sparse CT data for projection using CS theories, proposes to combine total variance (Total
Variation, TV) minimize and Algebraic Iterative Method (Algebraic Reconstruction Technique, ART) carry out it is dilute
CT image reconstruction data ART-TV algorithms are dredged, CT image reconstructions quality under sparse projection data is effectively increased.General original graph
The total variance of picture cannot constrain the solution of image reconstruction model well, when 0<p<When 1, LpPact of the norm to image reconstruction model solution
Beam is stronger, and using Lp norms to CT image reconstructions, if finding, p value is too small, and CT image reconstruction will produce more apparent artifact, noise
Greatly, reconstructed image quality is relatively low；If p value is excessive, CT image reconstruction tends to be fuzzy, and micro-structure display effect is poor, rebuilds
Effect is poor.When p values are during [0.4,0.6], the average gradient of reconstruction image, edge strength and entropy are larger, explanation
The clarity of its reconstruction image is high, signal-to-noise ratio is big, details is clear, artifact is few, and it is good to rebuild effect.
Invention content
Technical problem：The object of the present invention is to provide a kind of compressed sensing CT image rebuilding methods based on P norms, overcome
Algebraic Iterative Method obscures that ghost image is heavier and algorithm takes the shortcomings of more in the case of incomplete sampled data in CT images, really
Protect reconstructed image quality.Moreover, the CT scan time can be reduced, reduce the X-ray exposure time by sampling a small amount of data for projection, reduce
Injury to testee.
Technical solution：The compressed sensing computed tomography images method for reconstructing based on P norms of the present invention is algebraically
The computer tomography CT image rebuilding method of iterative approximation combination compressed sensing；First, CT data for projection is obtained；Then just
Beginningization CT data for projection carries out sliding-model control and filtering noise reduction process using wavelet transformation base to data for projection；Then, right
Data for projection carries out more wheel Image Iteratives reconstructions after initialization, and total variance is done to the image after each iteration using gradient descent method
Lp norm minimums adjust, and judge whether reconstruction image meets iteration convergence condition, if not satisfied, then carrying out next round iteration；
If satisfied, then reconstruction image is used as to preserve output；Wherein, Lp norms refer to given vector y=y1, y2... ys, s is natural number,
For opening p powers after the p powers summation of each element absolute value of vector.
It is realized using wavelet transformation base and sliding-model control is carried out to original undersampling projection data, constructed Hadamard first and become
It changes random matrix and multiple random measurement is carried out to be far below Nyquist sampling frequency to sparse signal, process is made to meet constraint etc.
Away from property condition, Lp norm minimums are carried out to wavelet conversion coefficient.
It is described total variance Lp norm minimums are done to the image after each iteration using gradient descent method to be adjusted to：
Formula 1), formula 2) in, xI, jIt refer to the grey scale pixel value that image x is arranged in the i-th row, jthIndicate the full variation of image x
Convert the derivation to gray value；dAIndicate the estimation image before data for projection iterative process and the image data after positive number constraint
Difference；α is regulatory factor；The decrement for indicating iterative calculation TV gradients, is repeated calculating, until n=N；N tables
Show that gradient descent method iteration serial number, N indicate the required calculation times of gradient descent method.
Judge whether reconstruction image meets iteration convergence condition and be：dAWhether value is a minimum, i.e. dAIt is fully small, or work as
Iterations terminate interative computation after reaching maximum；Otherwise next round interative computation is carried out.
The selection of p value has an impact image reconstruction quality in the Lp norms, when during p values are in [0,0.3], rebuilds
CT images will produce overlapping shade, and signal-to-noise ratio is in [19.5946db, 24.9503db], and reconstruction image shows fuzzy；When p values
When during [0.5,1], CT image reconstruction tends to be fuzzy, micro-structure loss of detail；When during p values are in [0.4,0.6],
Average gradient, the edge strength of reconstruction image are respectively increased 33% and 20%, reconstruction image signal-to-noise ratio be in [26.3314db,
27.127db], the details of image is shown clearly, while the artifact for influencing reconstructed image quality is also not present, and is rebuild effect and is made us
It is satisfied.Advantageous effect：Image total variance TV regularization algorithms can carry out undersampling projection data in compressive sensing theory
Full images are rebuild, and are ensured that all important feature form sawtooth artifacts of reconstruction image reservation are heavier, can be reduced CT imaging systems and sweep
The time is retouched, the X-ray exposure time is reduced, accelerates image taking speed, to reduce machine cost, and reduces and is detected object motion artifacts,
Expand clinical application range.
Specific implementation mode
First, CT data for projection is obtained and is initialized, including sparse transformation and image sampling；Then, to initialization
Data for projection carries out the m wheel Image Iterative reconstructions of total variance adjustment afterwards.Image total variance Lp Norm minimums are done to image after iteration
The adjustment of change, judges m (0<m<M) whether wheel iterative approximation image meets iteration convergence condition, if being unsatisfactory for iteration convergence item
Part then continues iteration；If satisfied, then reconstruction image is preserved and is exported.
Small echo sparse transformation realizes that the rarefaction representation to sampling image data, image sampling refer to meeting to constrain using one
Equidistant condition and irregular Local Fourier Transform matrix image sampling.
Image total variance TV such as formulas 1)
Wherein：
dA=| | xART(0)-xART(m)|| 3)
Judge to adjust whether image meets iterated conditional：dAWhether it is a minimum, i.e. dAIt is fully small, or when iteration time
After number reaches maximum iteration, terminates interative computation, preserve and export image；Otherwise next round is carried out using Algebraic Iterative Method
Interative computation.
A kind of compressed sensing CT image rebuilding methods based on P norms of the present invention specifically comprise the following steps：
1. obtaining CT scan device parameter, acquisition CT is imaged Raw projection data；
2. the Raw projection data that initialization step 1 is obtained, mainly including the use of wavelet transformation base to data for projection into
Row reconstruction image discretization and filtering noise reduction process, solve projection matrix by weighting and carry out assignment x to initial pictures x(0)
=0；Small echo sparse transformation realizes to the rarefaction representation of sampling image data, image sampling refer to using a Hadamard transform with
Machine matrix carries out image sampling.
3. the data for projection of initialization is filtered backprojection reconstruction, prior image is obtained；
4. being initialized：Setting algebraically iterations are M, and gradient descent method iterations are N, pine in Algebraic Iterative Method
The relaxation factor is set as λ, and assignment x is carried out to initial pictures x(0)=0；
5. carrying out an iteration operation using Algebraic Iterative Method：
Wherein, algebraically iterations serial number m=1,2 ..., M；Gradient descent method number serial number n=1,2 ..., N；αiIt indicates
I-th row data element in sytem matrix.
6. positive number constraint is added：
7. steepest descent method initializes：
dA=| | xART(0)-xART(m)|| (4)
8. being iterated operation along image gradient Lp norms, that is, image total variance gradient descent direction using gradient descent method：
Formula (5) is the gradient for calculating image total variance；Formula (6) is using gradient descent method along image gradient Lp norms
That is image total variance gradient descent direction is iterated operation, xijRefer to image x in the i-th row, the gray value of jth row pixel；
Indicate that the full variation of image x converts the derivation for gray value；dAIndicate data for projection iterative process before estimation image with just
The difference of image data after number constraint；α is regulatory factor；The decrement for indicating iterative calculation TV gradients, is repeated meter
It calculates, until n=N；N indicates that gradient descent method iteration serial number, N indicate gradient descent method calculation times.
9. working as dAWhen value is a minimum, i.e. dAIt is fully small, or after iterations reach maximum iteration, terminate
Interative computation preserves and exports image；If it is not, then carrying out next round iteration fortune using upper wheel result as initial value return to step 4
It calculates.
Claims (4)
1. a kind of compressed sensing computed tomography images method for reconstructing based on P norms, which is characterized in that this method is generation
The computer tomography CT image rebuilding method of number iterative approximation combination compressed sensing；First, CT data for projection is obtained；Then
CT data for projection is initialized, sliding-model control and filtering noise reduction process are carried out to data for projection using wavelet transformation base；Then,
More wheel Image Iteratives are carried out to data for projection after initialization to rebuild, and total change is done to the image after each iteration using gradient descent method
Poor Lp norm minimums adjustment, judges whether reconstruction image meets iteration convergence condition, changes if not satisfied, then carrying out next round
Generation；If satisfied, then reconstruction image is used as to preserve output；Wherein, Lp norms refer to given vector y=y1, y2... ys, s is nature
Number, for opening p powers after the p powers summation of each element absolute value of vector；Using wavelet transformation base to data for projection carry out from
Constructed first in dispersion processing step Hadamard transform random matrix to sparse signal be far below Nyquist sampling frequency into
The multiple random measurement of row, makes Hadamard transform random matrix meet constraint isometry condition, and Lp models are carried out to wavelet conversion coefficient
Number minimizes.
2. the compressed sensing computed tomography images method for reconstructing according to claim 1 based on P norms, feature
It is, it is described total variance Lp norm minimums are done to the image after each iteration using gradient descent method to be adjusted to：
Formula 1), formula 2) in, xI, jIt refer to the grey scale pixel value that image x is arranged in the i-th row, jth；Indicate the full variation transformation of image x
Derivation to gray value；dAIndicate the difference of the estimation image before data for projection iterative process and the image data after positive number constraint
It is different；α is regulatory factor；The decrement for indicating iterative calculation TV gradients, is repeated calculating, until n=N；N is indicated
Gradient descent method iteration serial number, N indicate the required calculation times of gradient descent method.
3. the compressed sensing computed tomography images method for reconstructing according to claim 1 based on P norms, feature
It is, judges whether reconstruction image meets iteration convergence condition and be：dAWhether value is a minimum, i.e. dAIt is fully small；Wherein, dA
Indicate the difference of the estimation image before data for projection iterative process and the image data after positive number constraint；Or when iterations reach
Terminate interative computation after maximum；Otherwise next round interative computation is carried out.
4. the compressed sensing computed tomography images method for reconstructing according to claim 1 based on P norms, feature
Be, in the Lp norms selection of p value have larger impact to image reconstruction quality, if p value is too small, CT image reconstruction will produce
More apparent artifact, noise is big, and reconstructed image quality is relatively low；If p value is excessive, CT image reconstruction tends to be fuzzy, and micro-structure is aobvious
Show that effect is poor, it is poor to rebuild effect；When p values are in [0.4,0.6] section, average gradient, the edge strength of reconstruction image
Take other values larger relatively with entropy, i.e., the information content that image carries is larger；The noise of reconstruction image is bigger simultaneously, indicates
The noisiness that reconstruction image includes is relatively low, and the details of image is shown clearly, while too many influence reconstructed image quality is also not present
Artifact.
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