CN109375125A - A kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter - Google Patents
A kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter Download PDFInfo
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- CN109375125A CN109375125A CN201811247095.1A CN201811247095A CN109375125A CN 109375125 A CN109375125 A CN 109375125A CN 201811247095 A CN201811247095 A CN 201811247095A CN 109375125 A CN109375125 A CN 109375125A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
- G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/561—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution by reduction of the scanning time, i.e. fast acquiring systems, e.g. using echo-planar pulse sequences
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
- G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/5608—Data processing and visualization specially adapted for MR, e.g. for feature analysis and pattern recognition on the basis of measured MR data, segmentation of measured MR data, edge contour detection on the basis of measured MR data, for enhancing measured MR data in terms of signal-to-noise ratio by means of noise filtering or apodization, for enhancing measured MR data in terms of resolution by means for deblurring, windowing, zero filling, or generation of gray-scaled images, colour-coded images or images displaying vectors instead of pixels
Abstract
It is a kind of correct regularization parameter compressed sensing magnetic resonance imaging method for reconstructing belong to field of image processing；Including fetching portion K space data；Utilize full variation transformation model theory building MR image reconstruction objective function；Using the method for solving of alternating direction Multiplier Algorithm, auxiliary variable regularization coefficient balance regular terms and data constraint item are introduced, the optimization problem of objective function is changed into the Solve problems of subfunction；Update alternating direction Multiplier Algorithm subproblem；Update Lagrange multiplier；Modifying factor is added, corrects regularization parameter, balances regular terms and data item；Judge whether to need to be added modifying factor and the size of modifying factor is added, updates subproblem solving result and regularization parameter, update Lagrange multiplier；Judge whether to meet stopping criterion for iteration, meet condition, then terminate iteration, obtains the magnetic resonance image finally rebuild；The magnetic resonance imaging time can be effectively reduced, and then solves the technical issues of causing because of magnetic resonance imaging time length.
Description
Technical field
The invention belongs to field of image processing more particularly to a kind of compressed sensing magnetic resonance imagings for correcting regularization parameter
Method for reconstructing.
Background technique
Mr imaging technique (Magnetic Resonance Imaging, MRI) is auxiliary as the present age most important medical treatment
One of assistant's section.However there is problems urgently to be resolved for MRI imaging technique.The most important defect of MRI is exactly the signal acquisition time
It is too long, it requires patient totally stationary during scanning, otherwise can generate motion artifacts.Too long sweep time and reconstitution time is same
Utilization rate of equipment and installations can be reduced, clinical throughputs are reduced, so as to cause operation cost valuableness.For this purpose, MRI fast imaging need to be studied.
Summary of the invention
The present invention overcomes above-mentioned the deficiencies in the prior art, provide a kind of compressed sensing magnetic resonance for correcting regularization parameter
Imaging reconstruction method can carry out Exact Reconstruction to magnetic resonance image using less k-space scan data, can effectively reduce magnetic
The resonance image-forming time, and then solve the technical issues of causing because of magnetic resonance imaging time length.
Technical solution of the present invention:
A kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter, including the following steps:
Step a, fetching portion K space data；
Step b, full variation transformation model theory building MR image reconstruction objective function is utilized；
Step c, auxiliary variable canonical is introduced using the method for solving of alternating direction Multiplier Algorithm according to the objective function of construction
Change coefficient equilibrium regular terms and data constraint item, the optimization problem of objective function is changed into the Solve problems of subfunction；
Step d, alternating direction Multiplier Algorithm subproblem is updated；
Step e, Lagrange multiplier is updated；
Step f, modifying factor is addedWith, correct regularization parameterValue, balance regular terms and data item, execute step
Rapid d is iterated operation；
Step g, by the way that the reconstruction index in two neighboring stage in reconstruction process after modifying factor will be added, and modifying factor is not added
The reconstruction Indexes Comparison in two neighboring stage in the reconstruction process of son judges whether to need to be added modifying factor and modifying factor is added
The size of son updates subproblem solving result and regularization parameter, and executes step e, updates Lagrange multiplier；
Step h, judge whether to meet stopping criterion for iteration, if not satisfied, then returning to step f continues loop iteration behaviour
Make, if meeting condition, terminates iteration, obtain the magnetic resonance image finally rebuild.
Further, described to utilize full variation transformation model theory building MR image reconstruction objective function Equation such as
Under:
。
Further, the subfunction, which solves, uses Lagrange's equation, and formula is as follows:
。
Further, the update alternating direction Multiplier Algorithm subproblem formula is as follows:
。
Further, the update Lagrange multiplier formula is as follows:
。
Further, after the addition modifying factorIt is transformed to following form:
Wherein、For modifying factor, and, index is rebuild according to adjacent image in an iterative process and judges whether needs
Modifying factor corrects regularization coefficientValue；
The subproblem of alternating direction Multiplier Algorithm and the solution of Lagrange multiplier are transformed to following form:
。
Further, the reconstruction index uses Y-PSNR and the dual reconstruction index of structural similarity, by comparing
The Y-PSNR and structural similarity of the adjacent phases reconstruction image of former regularization coefficient and addition amendment regularization coefficient, sentence
It is disconnected whether modifying factor to be added；
Former regularization coefficient subproblem solution procedure is as follows:
It is as follows to correct regularization coefficient subproblem solution procedure:
If meeting condition, then update,,；
It is adjusted back if being unsatisfactory for condition and solves subproblem:
If meeting condition, then update,,；
It is updated if being unsatisfactory for condition,,。
The present invention has the advantages that compared with the existing technology
The present invention provides a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter, compared to traditional doctor
Image reconstruction algorithm is learned, the present invention is reconstructed using less sampled data high-precision from signal sparsity angle
Magnetic resonance image reduces the number of samples of data, reduces subsequent data transmission, processing and amount of storage, and better meet
Accelerate the growth requirement of medical imaging speed.
Compressive sensing theory is applied in magnetic resonance imaging by the present invention, can be right using less k-space scan data
Magnetic resonance image carries out Exact Reconstruction, can effectively reduce the magnetic resonance imaging time, and then solves due to magnetic resonance imaging time length
The technical issues of initiation.
Detailed description of the invention
Fig. 1 is flow chart of the present invention；
Fig. 2 is magnetic resonance MRI brain image and contrast and experiment used in emulation experiment；
Fig. 3 is the comparison diagram of reconstructed results and original image；
Fig. 4 is the Y-PSNR and structural similarity figure of reconstructed results.
Specific embodiment
Below with reference to attached drawing, the present invention is described in detail.
Specific embodiment one
A kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter, as shown in Figure 1, including the following steps:
Step a, fetching portion K space data；
Step b, full variation transformation model theory building MR image reconstruction objective function is utilized；
Step c, auxiliary variable canonical is introduced using the method for solving of alternating direction Multiplier Algorithm according to the objective function of construction
Change coefficient equilibrium regular terms and data constraint item, the optimization problem of objective function is changed into the Solve problems of subfunction；
Step d, alternating direction Multiplier Algorithm subproblem is updated；
Step e, Lagrange multiplier is updated；
Step f, modifying factor is addedWith, correct regularization parameterValue, balance regular terms and data item, execute
Step d is iterated operation；
Step g, by the way that the reconstruction index in two neighboring stage in reconstruction process after modifying factor will be added, and modifying factor is not added
The reconstruction Indexes Comparison in two neighboring stage in the reconstruction process of son judges whether to need to be added modifying factor and modifying factor is added
The size of son updates subproblem solving result and regularization parameter, and executes step e, updates Lagrange multiplier；
Step h, judge whether to meet stopping criterion for iteration, if not satisfied, then returning to step f continues loop iteration behaviour
Make, if meeting condition, terminates iteration, obtain the magnetic resonance image finally rebuild.
Using compressive sensing theory, the limitation of Nyquist sampling thheorem is breached, as long as signal is compressible or at certain
A transform domain is data reconstruction original signal that is sparse, just being required using Nyquist sampling thheorem is far below.The present invention will press
Contracting perception theory is rebuild applied to medical image, significant effect.
Compressed sensing based signal reconstruction is theoretical are as follows:
(1)
Wherein, b indicates the observation data after sub-sampling,Indicate calculation matrix,Indicate that sparse matrix, s indicate sparse
Coefficient.Min is the professional term of minimization problem, and it is a professional term that s.t., which is subject to, min | | s | |1It is
It minimizesExpression formula, therefore, compressed sensing problem is exactly in known measurements b, calculation matrix, sparse matrixItem
Under part, it is converted into minimum The problem of norm is the convex optimization problem of standard, can solve to ask with the method for convex optimization
Topic.
In image reconstruction, the image of reconstruction need to meet following relationship:
(2)
Wherein, b indicates the observation data after sub-sampling,It is image to be reconstructed,It is measurement square
Battle array,It is noise in measurement data, it may be assumed that
(3)
Noise is added, formula (1) is changed into
(4)
Wherein,The reconstruction of this kind of image is not present in solution for the Frobenius norm of representing matrix
In the case of, approximate optimal solution can be sought, basic MRI reconstruction model is constructed by increase attaching means:
(5)
Wherein,Indicate sparse regularization term,Indicate sparse regularization coefficient,It is image to be reconstructed；Its
In sparse regular terms use full variation transformation model, full variation image is discrete gradient changing image, be suitable for Piecewise Smooth,
The apparent medical image of profile.
Mathematical model is as follows
(6)
Wherein,Indicate full variational regularization item, expression formula are as follows:
(7)
WhereinIndicate image to be reconstructed.
The present invention is introduced using the thought of alternately Multiplier Algorithm when handling the reconstruction model based on full variation regular terms
Auxiliary variableSeparable structure is constructed, optimization method is as follows
(8)
WhereinIt is defined as,,It is for image sizeMRI image on two dimensions
Gradient information, concrete form is as follows:
(9)
Wherein,,The index of representative image pixel on two dimensions, formula (8) augmentation Lagrange's equation
Are as follows:
(10)
WhereinFor Lagrange multiplier,> 0 is regularization coefficient,,> 0 is data constraint item parameter.
Optimization problem specific steps are iteratively solved using alternately Multiplier Algorithm are as follows:
(11)
Wherein, k indicates kth time iteration,,,The solution of subproblem, further spreads out formula after expression kth time iteration are as follows:
(12)
In traditional algorithm, regularization coefficientValue be fixed value, play the role of balance regular terms, due to Exact Reconstruction figure
As the energy difference of reconstruction signal in the process two neighboring stageBe it is gradually small, illustrate that two neighboring stage rebuilds
The energy difference of image initial stage decline quickly, in fall very little later, it is finally stable within a certain range.This hair
Modifying factor is added in the bright energy difference changing rule according to adjacent phases reconstruction signal,, correct regularization parameterTake
Value balances regular terms and data item, proposes a kind of based on the alternative manner for becoming regularization coefficient.
After modifying factor is addedIt is transformed to following form:
,(13)
WhereinIndicate the value that regularization parameter is corrected when kth time iteration,,() it is modifying factor,、For
The index of modifying factor respectively indicates amendment regularization parameter and is corrected the factor,Modified number, in an iterative process root
Y-PSNR (PSNR) and structural similarity (SSIM) in index is rebuild according to adjacent image to judge whether that modifying factor is needed to repair
Positive regularization coefficientValue.
Then the subproblem of alternating direction Multiplier Algorithm and the solution of Lagrange multiplier are transformed to following form:
(14)
Wherein, the present invention uses Y-PSNR and the dual reconstruction index of structural similarity, by comparing former regularization coefficient and
The Y-PSNR and structural similarity of the adjacent phases reconstruction image of amendment regularization coefficient is added, judges whether that amendment is added
The factor.
Former regularization coefficient subproblem solution procedure is as follows:
(15)
Wherein,、Respectively indicate useThe solution of each subproblem is solved, regularization coefficient subproblem solution procedure is corrected
It is as follows:
(16)
Wherein,It indicates to use modifying factorRevised regularization coefficient,、Respectively indicate useIt solves each
The solution of subproblem, if meeting condition, then update,,；
It is adjusted back if being unsatisfactory for condition and solves subproblem:
(17)
Wherein,It indicates to use modifying factorRevised regularization coefficient,、Respectively indicate useIt solves each
The solution of subproblem, if meeting condition, then update,,；
It is updated if being unsatisfactory for condition,,
Update Lagrange multiplier
(18)
Judge whether to meet stopping criterion for iteration, returned if being unsatisfactory for and continue cycle iterative operation thereof, if meeting condition
Iteration is terminated, the magnetic resonance image finally rebuild is obtained.
Specific embodiment two
Embodiment algorithm for reconstructing selects ADMM algorithm, and reconstruction image chooses brain MRI image, and image size is,
Implementation step is as follows:
1, known calculation matrix uses radial measurement matrix, initialization process is carried out to the K spatial observation data of lack sampling, to it
Carry out inversefouriertransform, the initialisation image x after being rebuild.
2, initiation parameter,,,,,,,,。
3, subproblem is solved using alternately Multiplier Algorithm and update Lagrange multiplier initial value,:
4, using regularization parameterSubproblem is solved:
5, modifying factor is added, amendment regularization coefficient solution subproblem:
6, Y-PSNR and the dual reconstruction index of structural similarity are set, is repaired by being respectively compared former regularization coefficient and addition
The Y-PSNR and structural similarity of the adjacent phases reconstruction image of positive regularization coefficient judge whether that modifying factor is added.
If meeting condition, then update,,；
7, it is adjusted back if being unsatisfactory for condition and solves subproblem:
If meeting condition, then update,,；
It is updated if being unsatisfactory for condition,,
8, Lagrange multiplier is updated:
9, judge whether to meet stopping criterion for iteration, 7 are returned to step if being unsatisfactory for and continues cycle iterative operation thereof, if
Meet condition and then terminate iteration, obtains the magnetic resonance image finally rebuild.
The present invention uses structural similarity, Y-PSNR and relative error (Relative Error) as evaluation image
The index of quality, from the quality of subjective and objective angle evaluation picture quality.
Reconstruction image effect picture when Fig. 2 is sample rate 0.2, the first width is that size is in Fig. 2Brain magnetic it is total
Shake image, and the second width and third width are respectively the reconstruction effect picture of inventive algorithm and ADMM+TV algorithm, it can be seen that individually
ADMM+TV algorithm be distorted at details it is more obvious, no matter in smooth region or details area, it can be seen that of the invention
The algorithm of offer is rebuild effect compared with ADMM+TV algorithm and is more clear, after Fig. 3 is inventive algorithm and the reconstruction of ADMM+TV algorithm
Relative error figure can significantly find out that the relative error of inventive algorithm will be far smaller than ADMM+TV algorithm.
Fig. 4 is algorithm provided by the invention reconstruction image under different sample rates from ADMM+TV algorithm under the same terms
Quality versus.It is promoted compared with ADMM+TV algorithm as can be seen that the present invention rebuilds index in different sample rates, wherein peak
Value signal-to-noise ratio averagely promotes 2.6dB, and structural similarity averagely promotes 0.0387.The mentioned method of this civilization under subjective and objective angle
It is superior to analogous algorithms.
It will be appreciated by those skilled in the art that embodiment described above should be special statement be not intended to limit it is of the invention
Protection scope, any modification, equivalent substitution, improvement and etc. done all within the spirits and principles of the present invention, should be included in
Within scope of the presently claimed invention.
Claims (7)
1. a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter, characterized in that it comprises the following steps:
Step a, fetching portion K space data；
Step b, full variation transformation model theory building MR image reconstruction objective function is utilized；
Step c, auxiliary variable canonical is introduced using the method for solving of alternating direction Multiplier Algorithm according to the objective function of construction
Change coefficient equilibrium regular terms and data constraint item, the optimization problem of objective function is changed into the Solve problems of subfunction；
Step d, alternating direction Multiplier Algorithm subproblem is updated；
Step e, Lagrange multiplier is updated；
Step f, modifying factor is addedWith, correct regularization parameterValue, balance regular terms and data item, execute step
Rapid d is iterated operation；
Step g, by the way that the reconstruction index in two neighboring stage in reconstruction process after modifying factor will be added, and modifying factor is not added
The reconstruction Indexes Comparison in two neighboring stage in the reconstruction process of son judges whether to need to be added modifying factor and modifying factor is added
The size of son updates subproblem solving result and regularization parameter, and executes step e, updates Lagrange multiplier；
Step h, judge whether to meet stopping criterion for iteration, if not satisfied, then returning to step f continues loop iteration behaviour
Make, if meeting condition, terminates iteration, obtain the magnetic resonance image finally rebuild.
2. a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter according to claim 1, feature
It is, described as follows using full variation transformation model theory building MR image reconstruction objective function Equation:
。
3. a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter according to claim 1, feature
It is, the subfunction, which solves, uses Lagrange's equation, and formula is as follows:
。
4. a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter according to claim 1, feature
It is, the update alternating direction Multiplier Algorithm subproblem formula is as follows:
。
5. a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter according to claim 1, feature
It is, the update Lagrange multiplier formula is as follows:
。
6. a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter according to claim 5, feature
It is, after the addition modifying factorIt is transformed to following form:
Wherein、For modifying factor, and, index is rebuild according to adjacent image in an iterative process and judges whether needs
Modifying factor corrects regularization coefficientValue；
The subproblem of alternating direction Multiplier Algorithm and the solution of Lagrange multiplier are transformed to following form:
。
7. a kind of compressed sensing magnetic resonance imaging method for reconstructing for correcting regularization parameter according to claim 1, feature
It is, the reconstruction index uses Y-PSNR and the dual reconstruction index of structural similarity, by comparing former regularization coefficient
With the Y-PSNR and structural similarity of the adjacent phases reconstruction image that amendment regularization coefficient is added, judges whether to be added and repair
Positive divisor；
Former regularization coefficient subproblem solution procedure is as follows:
It is as follows to correct regularization coefficient subproblem solution procedure:
If meeting condition, then update,,；
It is adjusted back if being unsatisfactory for condition and solves subproblem:
If meeting condition, then update,,；
It is updated if being unsatisfactory for condition,,。
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| CN115563444A (en) * | 2022-12-06 | 2023-01-03 | 苏州浪潮智能科技有限公司 | Signal reconstruction method and device, computer equipment and storage medium |
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| CN111047661A (en) * | 2019-12-12 | 2020-04-21 | 重庆大学 | CS-MRI image reconstruction method based on sparse manifold joint constraint |
| CN114125471A (en) * | 2021-11-27 | 2022-03-01 | 北京工业大学 | Video coding pre-filtering method |
| CN115563444A (en) * | 2022-12-06 | 2023-01-03 | 苏州浪潮智能科技有限公司 | Signal reconstruction method and device, computer equipment and storage medium |
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