CN109636725A - A kind of super-resolution reconstruction method of magnetic resonance diffusion sequence spectrum - Google Patents
A kind of super-resolution reconstruction method of magnetic resonance diffusion sequence spectrum Download PDFInfo
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Abstract
A kind of super-resolution reconstruction method of magnetic resonance diffusion sequence spectrum, is related to magnetic resonance diffusion sequence spectrum.It constructs magnetic resonance diffusion sequence and composes sparse reconstruction model；There to be restricted model to be melted into unrestricted model；Initiation parameter t and x；Circulation executes following sub-step: 1. calculating the solution of newton system of linear equations as descent direction Δ x using PCG algorithm；2. calculating decline step-length s using backtracking straight-line method；3. updating iterative value x=x+s Δ x；4. constructing antithesis feasible point v；5. judging whether η/G (v) is less than preset accuracy value ε=10‑8, if satisfied, then exiting circulation.6. updating t, and jump back to step 1.；Spectrogram x is rebuild in output.
Description
Technical field
The present invention relates to magnetic resonance to spread sequence spectrum, and the high-resolution weight of sequence spectrum is spread more particularly, to a kind of magnetic resonance
Construction method.
Background technique
Magnetic resonance diffusion sequence spectrum is widely used in clinical medicine and field of biotechnology, can be used for identifying in mixture
Molecular species, structure and quantitative analysis.A diffusion sequence spectrum is obtained, needing will be under gradient field strength different in diffusion experiment
The signal adopted carries out the extraction and analysis of attenuation constant, and spectral peak signal strength is pair with the decaying that gradient field strength increase generates
Answer the diffusion coefficient of substance.Traditional diffusion coefficient calculation method generally uses mono-exponential fit method, i.e., by each gradient fields
Each spectral peak signal strength and the single index signal measured under intensity is fitted, and the applicable premise of this method is a chemical shift
Frequency location (i.e. a spectral peak) corresponds to a diffusion coefficient.But for complex sample, a chemical shift is often corresponded to
Multiple diffusion coefficients (there is the case where peak overlap).In this case, traditional mono-exponential fit method often can not be quasi-
Really calculate acquisition diffusion coefficient.The case where for peak overlap, researcher propose reverse drawing Laplace transform spectrum reconstruction side
Method is calculated and is analyzed to be diffused coefficient.Although reverse drawing Laplace transform can have spectral peak in peak overlap
The phenomenon that effect is distinguished, but its diffusion sequence spectrum reconstructed often will appear spectral peak broadening, leads to the reduction of spectra resolution rate.
Summary of the invention
The purpose of the present invention is to provide excellent effects, a kind of magnetic resonance expansion that easily operated, reconstruction spectra resolution rate is high
Dissipate the super-resolution reconstruction method of sequence spectrum.
The present invention the following steps are included:
1) sparse reconstruction model is composed in building magnetic resonance diffusion sequence:
In formula (1), x is magnetic resonance to be reconstructed diffusion sequence spectrum, and K is Laplace transform matrix, and y declines for gradient fields
Cut signal, | | | |2For two norms of vector, | | | |1For a norm of vector, λ is a regularization parameter, for weighingWith | | x | |1Two importance,The fidelity of seizing signal, | | x | |1The sparsity of seizing signal.
2) restricted model is melted into unrestricted model formula (1):
In formula (2), log (x) is logarithmic barrier function, and for constraining the nonnegativity of x, its value is equal to vector x
Each element take using e as the sum of the logarithm at bottom, t is the parameter for controlling logarithmic barrier function specific gravity in a model.
3) initiation parameter t and x；
4) circulation executes following sub-step:
1. calculating newton system of linear equations using PCG (Preconditioner Conjugate Gradient) algorithm
Solution is used as descent direction Δ x, newton system of linear equations are as follows:
H Δ x=-g (3)
In formula (3), H and g are respectively Hessian matrix and gradient of formula (2) objective function in current iteration value x
Vector；
2. calculating decline step-length s using backtracking straight-line method；
3. updating iterative value x=x+s Δ x；
4. constructing antithesis feasible point v, duality gap is calculatedWherein, G (v) can be indicated
Are as follows:
G (ν)=- (1/4) vTv-vTy (4)
For the dual function of formula (1), antithesis feasible point v is constructed by following formula (5):
In formula (5), subscript i indicates that i-th of element of vector, m are the total length of gradient fields deamplification y；
5. judging whether η/G (v) is less than preset accuracy value ε=10-8, if satisfied, then exiting circulation.
6. updating t, and jump back to step 1.；
Rule is updated to use:
In formula (6), selection parameter μ=2, smin=0.5；M is the length of vector y.
5) spectrogram x is rebuild in output.
The present invention carries out reverse drawing Laplace transform using L1 norm dilute with the sparse characteristic of magnetic resonance diffusion sequence spectrum
Regularization constraint is dredged, sparse reconstruction model is constructed, and for the first time using truncation newton interior point method (Truncated Newton
Interior Point Method, TNIPM) sparse reconstruction model is solved.Method for reconstructing of the present invention is both applicable to compose
The case where overlap of peaks, solves traditional mono-exponential fit method for reconstructing and is applying upper limitation, and can make to rebuild spectrogram holding spectrum
Peak is sharp, high-resolution, solves the problems, such as that reverse drawing Laplace transform spectral peak broadens and low resolution.The invention is easy to operate, fits
Wide with range, the spectra resolution rate reconstructed is high, has very big application prospect.
The present invention proposes a kind of based on truncation newton interior point method (Truncated Newton Interior Point
Method, TNIPM) magnetic resonance diffusion sequence spectrum sparse reconstruction method.The spectrum that existing diffusion sequence spectrum algorithm for reconstructing obtains
Figure is excessively smooth, and spectral peak broadening causes spectra resolution rate lower.It is an object of the invention to establish and solve diffusion sequence spectrum
Sparse reconstruction model realizes that high-resolution spectrogram is rebuild.The invention firstly uses gradient fields decay factors to generate Laplace transform
Matrix, and the sparse characteristic based on diffusion sequence spectrum carries out regularization constraint, then carries out model optimization using TNIPM algorithm,
To reconstruct high-resolution diffusion sequence spectrogram.In the process, the present invention combines and combines data fidelity and spectrum
The sparse characteristic of figure establishes sparse model, and is creatively iterated optimization using TNIPM algorithm, and the spectrogram reconstructed can be with
Solve the problems, such as the indistinguishable overlap peak that traditional mono-exponential fit method is encountered, and spectral peak is sharp, precision is high, to reach
To high-resolution effect.The present invention for the first time applies to TNIPM algorithm in magnetic resonance diffusion sequence spectrum reconstruction, simple and convenient,
Excellent effect, the final High resolution reconstruction for realizing magnetic resonance diffusion sequence spectrum.
Detailed description of the invention
Fig. 1 is the desired reference spectrum for emulating magnetic resonance diffusion sequence spectrum.
Fig. 2 is the sparse reconstruction spectrum of PDCO.
Fig. 3 is the spectrum rebuild according to the method for the present invention.
Specific embodiment
Following embodiment will the present invention is further illustrated in conjunction with attached drawing.
Following embodiment will rebuild One-Dimension Magnetic resonance diffusion sequence spectrum emulation signal, include two spectral peaks.Gradient fields decaying
Signal sampling points are 32 points, are equal to 32 different gradient field strengths of ascending selection in experiment.Specific step is as follows:
1) sparse reconstruction model is composed in building magnetic resonance diffusion sequence:
In formula (1), x is magnetic resonance to be reconstructed diffusion sequence spectrum, and K is the Laplace transform square of dimension 32 × 300
Battle array, y is the gradient fields deamplification that dimension is 300 × 1, | | | |2For two norms of vector, | | | |1For a norm of vector, λ
=0.001 is regularization parameter, for weighingWith | | x | |1Two importance,The guarantor of seizing signal
True property, | | x | |1The sparsity of seizing signal.
2) restricted model is melted into unrestricted model formula (1):
In formula (2), log (x) is logarithmic barrier function, and for constraining the nonnegativity of x, its value is equal to vector x
Each element take using e as the sum of the logarithm at bottom, t is the parameter for controlling logarithmic barrier function specific gravity in a model.
3) initiation parameter t=1, x=1.
4) circulation executes following sub-step:
1. calculating newton system of linear equations using PCG (Preconditioner Conjugate Gradient) algorithm
Solution is used as descent direction Δ x, newton system of linear equations are as follows:
H Δ x=-g (3)
In formula (3), H and g are Hessian matrix and gradient of formula (2) objective function in current iteration value x respectively
Vector.
2. calculating decline step-length s using backtracking straight-line method.
3. updating iterative value x=x+s Δ x.
4. constructing antithesis feasible point v, duality gap is calculatedWherein, G (v) can be indicated
Are as follows:
G (ν)=- (1/4) vTv-vTy (4)
For the dual function of formula (1).Antithesis feasible point v is constructed by following formula (5):
In formula (5), subscript i indicates that i-th of element of vector, m are the total length of gradient fields deamplification y.
5. judging whether η/G (v) is less than preset accuracy value ε=10-8, if satisfied, then exiting circulation.
6. updating t, and jump back to step 1..
Rule is updated to use:
In formula (6), selection parameter μ
=2, smin=0.5；M is the length of vector y.
5) spectrogram x is rebuild in output.
From Fig. 1~3 it is found that the sparse reconstruction of magnetic resonance diffusion sequence spectral peak ratio PDCO that the method for the present invention is rebuild is composed sharply.
Table 1 is desired reference spectrum, the sparse spectrum peak position for rebuilding spectrum and spectrum is rebuild according to the method for the present invention of PDCO.
Table 1
| Magnetic resonance diffusion sequence spectrum method for reconstructing | Spectrum peak position (unit: 10-11m2s-1) |
| Desired reference spectrum | 0.31、2.01 |
| The sparse reconstruction of PDCO | 0.21±0.15、2.20±0.35 |
| The method of the present invention | 0.31±0.01、2.01±0.01 |
As known from Table 1, the spectrum peak position ratio PDCO sparse reconstruction method of the method for the present invention assessment is accurate.As it can be seen that of the invention
Method can achieve the purpose that magnetic resonance diffusion sequence spectrum high-precision is rebuild compared to existing method for reconstructing.
Claims (1)
1. a kind of super-resolution reconstruction method of magnetic resonance diffusion sequence spectrum, it is characterised in that the following steps are included:
1) sparse reconstruction model is composed in building magnetic resonance diffusion sequence:
In formula (1), x is magnetic resonance to be reconstructed diffusion sequence spectrum, and K is Laplace transform matrix, and y is gradient fields decaying letter
Number, | | | |2For two norms of vector, | | | |1For a norm of vector, λ is a regularization parameter, for weighingWith | | x | |1Two importance,The fidelity of seizing signal, | | x | |1The sparsity of seizing signal；
2) restricted model is melted into unrestricted model formula (1):
In formula (2), log (x) is logarithmic barrier function, and for constraining the nonnegativity of x, its value is equal to the every of vector x
One element takes using e as the sum of the logarithm at bottom, and t is the parameter for controlling logarithmic barrier function specific gravity in a model；
3) initiation parameter t and x；
4) circulation executes following sub-step:
1. being made using the solution that PCG (Preconditioner Conjugate Gradient) algorithm calculates newton system of linear equations
For descent direction Δ x, newton system of linear equations are as follows:
H Δ x=-g (3)
In formula (3), H and g be respectively formula (2) objective function the Hessian matrix of current iteration value x and gradient to
Amount；
2. calculating decline step-length s using backtracking straight-line method；
3. updating iterative value x=x+s Δ x；
4. constructing antithesis feasible point v, duality gap is calculatedWherein, G (v) is indicated are as follows:
G (ν)=- (1/4) vTv-vTy (4)
For the dual function of formula (1), antithesis feasible point v is constructed by following formula (5):
In formula (5), subscript i indicates that i-th of element of vector, m are the total length of gradient fields deamplification y；
5. judging whether η/G (v) is less than preset accuracy value ε=10-8, if satisfied, then exiting circulation；
6. updating t, and jump back to step 1.；
Rule is updated to use:
In formula (6), selection parameter μ=2, smin=0.5, m are the length of vector y；
5) spectrogram x is rebuild in output.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105651803A (en) * | 2016-03-11 | 2016-06-08 | 厦门大学 | Two-dimensional diffusion-ordered nuclear magnetic resonance spectroscopy method used for any magnetic field environments |
| CN106780372A (en) * | 2016-11-30 | 2017-05-31 | 华南理工大学 | A kind of weight nuclear norm magnetic resonance imaging method for reconstructing sparse based on Generalized Tree |
| CN107328804A (en) * | 2017-07-21 | 2017-11-07 | 中国科学院山西煤炭化学研究所 | A kind of magnetic resonance detection method of glycerine hydrogenation reactant mixture |
| CN108303439A (en) * | 2018-03-16 | 2018-07-20 | 浙江大学 | The test method of fluoride diffusion sequence spectrum based on nuclear magnetic resonance technique |
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2018
- 2018-12-13 CN CN201811525909.3A patent/CN109636725B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105651803A (en) * | 2016-03-11 | 2016-06-08 | 厦门大学 | Two-dimensional diffusion-ordered nuclear magnetic resonance spectroscopy method used for any magnetic field environments |
| CN106780372A (en) * | 2016-11-30 | 2017-05-31 | 华南理工大学 | A kind of weight nuclear norm magnetic resonance imaging method for reconstructing sparse based on Generalized Tree |
| CN107328804A (en) * | 2017-07-21 | 2017-11-07 | 中国科学院山西煤炭化学研究所 | A kind of magnetic resonance detection method of glycerine hydrogenation reactant mixture |
| CN108303439A (en) * | 2018-03-16 | 2018-07-20 | 浙江大学 | The test method of fluoride diffusion sequence spectrum based on nuclear magnetic resonance technique |
Non-Patent Citations (3)
| Title |
|---|
| BINYUAN 等: "Reconstructing diffusion ordered NMR spectroscopy by simultaneous inversion of Laplace transform", 《JOURNAL OF MAGNETIC RESONANCE》 * |
| ENPING LIN 等: "High-Resolution Reconstruction for Multidimensional Laplace NMR", 《THE JOURNAL OF PHYSICAL CHEMISTRY LETTERS》 * |
| 袁斌: "核磁共振扩散排序谱新方法", 《中国博士学位论文全文数据库 工程科技I辑》 * |
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