CN101051075A - Magnetic resonant part K data image re-establishing method based on compound strange spectrum analysis - Google Patents

Abstract

A method for restructuring partial K data of magnetic resonance based on complex singular spectral analysis includes setting up magnetic resonant image mathematic model of complex coefficient weighting singular function and complex singular spectral analysis model, using partial K data information to carry out model parameter estimation and then utilizing said mathematic model and said spectral analysis model to carry out restructuring of magnetic resonant image.

Description

Magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis

Technical field

The present invention relates to medical imaging detection technique field, particularly the mr imaging technique field specifically is meant a kind of magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis.

Background technology

Continuous development along with the modern medicine technology, Magnetic resonance imaging (MRI) technology has become means indispensable in the medical imaging detection range, wherein, magnetic resonance signal space (original data space) is called the K space, be the Fourier transform space, the K spatial sampling through delivery again after the Fourier inversion, promptly obtains nuclear magnetic resonance (MR) image to signal.The imaging of Partial K spatial data can improve sweep velocity exponentially under the constant prerequisite of hardware and scan mode.In K rectangular space coordinate grid (KCG) scanning, minimizing phase encoding number can add fast scan speed and (see also document: P.Margosian, F.Schmitt, D.Purdy, " Faster MR Imaging:Imaging with Half the Data; " Health Care Instrum., vol.1, pp.195-197,1986., with J.van Cuppen and A.van Est, " Reducing MR imaging time by one-sidedreconstruction, " Mag.Reso.Imag., vol.5, pp.526-527,1987.).It is the imaging strategy of a kind of collecting part K spatial data.Because magnetic resonance K spatial data is not to satisfy conjugate symmetry matter, promptly Hull rice property values (Hermitian) therefore cannot utilize symmetric relation to reduce the phase encoding number.Popular strategy is based on the Partial K spatial data image reconstruction of phase correction at present.Typical method has branch partly to compose POCS, phase correction conjugation balanced method and HM method or the like (see also document: E.M.Haacke, E.D.Lindskog, W.Lin, " A fast; iterative partial Fourier technique capable of localphase recovery; " J.Magn.Reson., vol.92, pp.126-145,1991., V.A.Stenger, D.C.Noll, F.E.Boada, " Partial k-space reconstruction for 3D gradient echo functional MRI:A comparison of phasecorrection methods; " Magn.Reson.Med., vol.40, pp.481-490,1998., D.C.Noll, D.G.Nishimura, A.Macovski, " Homodyne detection in magnetic resonance imaging, " IEEE Trans.Med.Imag., vol.10, pp.154-163,1991., and G.McGibney, M.R.Smith, S.T.Nicholas and A.Crawley; " Quantitativeevaluation of several partial-Fourier reconstruction algorithms used in MRI, " Magn.Reson.Med., vol.30; pp.51-59,1993.).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 low frequency K spatial data reconstruct, is used for phase correction then, thereby reaches the purpose of utilizing symmetry to replenish the K spatial data of not gathering.Be better than zero padding method imaging (the K space cartesian grid data of Cai Jiing are not filled up with zero, obtain the formation method of image space then with Fuli's leaf inverse transformation, cry the imaging of zero padding method) on this class methods general effect.

In the Partial K data imaging of HM method, conjugation balanced method and POCS method, its phase encoding scope is generally-n/16～n/2, and wherein n is due total phase encoding number.It only estimates phase place with the K data of usefulness-n/16～n/16 scope only, because if usefulness-n/16～n/2 estimation phase place will be because of the new phase error of the asymmetric introducing in K space.Its method is that the phase encoding district beyond right-n/16～n/16 is filled up with zero, carries out Fuli's leaf inverse transformation then, gets the phase estimation of image phase as entire image again.

Mainly there are following two shortcomings in the HM method:

(1) this phase estimation error is big, and figure has serious artefact usually, specifically sees also shown in Fig. 2 c, the 2d.

(2) this method of estimation prerequisite is that image phase changes slowly, and its phase frequency is in-n/16～n/16 scope, and the magnetic resonance image (MRI) phase place generally all is difficult to satisfy in image space everywhere, and the image of its reconstruct has the error that is difficult to expect.

The above distortion phenomenon that various shortcoming caused is enough to make the clinical diagnosis doctor to produce mistaken diagnosis, enter the gate that clinical medicine is used so that hamper them all the time, bring very big inconvenience so just for people's work and life, and limited further developing of medical imaging detection technique to a certain extent.

Summary of the invention

The objective of the invention is to have overcome above-mentioned shortcoming of the prior art, provide a kind of can Fast Reconstruction magnetic resonance complex pattern, effectively reduce image error, accurately show that former magnetic resonance image (MRI), highly effective, stable and reliable working performance, the scope of application are comparatively widely based on the magnetic resonant part K image reconstruction data method of multiple singular spectrum analysis.

In order to realize above-mentioned purpose, the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis of the present invention is as follows:

Should may further comprise the steps based on the magnetic resonant part K image reconstruction data method of multiple singular spectrum analysis:

(1) collecting part K data G (k) in the phase encoding scope of from magnetic resonance imagine scanner, presetting;

(2), carry out multiple singular spectrum analysis model parameter estimation according to these Partial K data;

(3), utilize the mathematical model and the multiple singular spectrum analysis model of the magnetic resonance image (MRI) of complex coefficient weighting singular function to carry out the reconstruct of magnetic resonance complex pattern according to the result of model parameter estimation.

Should be-N/16～N/2-1 that wherein N is the phase encoding number of complete K spatial data based on phase encoding scope of systemic presupposition in the magnetic resonant part K image reconstruction data method of multiple singular spectrum analysis.

Should be based on the magnetic resonance image (MRI) mathematical model of the complex coefficient weighting singular function in the magnetic resonant part K image reconstruction data method of multiple singular spectrum analysis:

$g\left(x\right)=\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{a}_q{w}_{b_q}\left(x\right),x=\mathrm{0,1},...,N-1;$

Wherein, g (x), x=0,1 ..., N-1 is a complex digital signal, { b ₁, b ₂..., b _QBe Q singular point on the g (x), { w _B1(x), w _B2(x) ..., w _BQ(x) } for respectively with { b ₁, b ₂..., b _QBe Q singular function of singular point, a ₁, a ₂..., a _QBe this Q singular point { b ₁, b ₂..., b _QOn multiple singular value.

Should be based on the multiple singular spectrum analysis model in the magnetic resonant part K image reconstruction data method of multiple singular spectrum analysis:

$G\left(k\right)=\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{a}_q{W}_{b_q}\left(k\right),k=\mathrm{0,1},...,N-1;$

Wherein, G (k)=DFT (g (x)), $W_{b_q}\left(k\right)=\mathrm{DFT}\left(w_{b_q}\left(x\right)\right),$ b _q=0,1 ..., Q, DFT () they are the discrete fourier transform operator.

Carrying out model parameter estimation in this magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis may further comprise the steps:

(1), and obtains Fourier spectrum data G after the missing data zero padding according to following formula to the disappearance part zero padding of these Partial K data G (k) _z(k):

G _z(k)＝G(k)R _s-e(k)；

Wherein, G (k) is signal g (x), x=0, and 1 ..., the Fourier spectrum data of N-1, k=-N/2-1 ..., N/2-1,

Be rectangular function, wherein s is for blocking upper limiting frequency, and e is for blocking lower frequency limit;

(2) calculate d according to following formula _z(x):

d _z(x)＝g _z(x)-g _z(x-1)；

Wherein, g _z(x)=DFT ^-1(G _z(k)), k=-N/2-1 ..., N/2-1, DFT ^-1The discrete Fuli's leaf inverse transformation operator of () expression;

(3) with resulting d _z(x) mould is according to ordering from big to small, and before getting L put as the unusual point set { b of preliminary election ₁, b ₂..., b _L, wherein L is rectangular function R _S-e(k) width, i.e. L=e-s, and known frequency spectrum are { G (k ₁), G (k ₂) ..., G (k _L);

(4) according to following formula construction singular spectrum equation:

(5) solve described singular spectrum equation with the pseudo inverse matrix method, obtain a least error and separate, obtain L plural singular value { a ₁, a ₂..., a _L;

(6) with { a ₁, a ₂..., a _LReturn as the result of model parameter estimation.

Be somebody's turn to do and carry out being reconstructed into of magnetic resonance complex pattern in the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis: can be based on the result { a of model parameter estimation ₁, a ₂..., a _L, according to the described complex digital signal g of following formula reconstruct (x):

$g\left(x\right)=\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{a}_q{w}_{b_q}\left(x\right),x=\mathrm{0,1},...,N-1;$

Perhaps, also can be based on the result { a of model parameter estimation ₁, a ₂..., a _L, according to following formula reconstruct described Fourier spectrum data G (k):

$G\left(k\right)=\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{a}_q{W}_{b_q}\left(k\right),k=\mathrm{0,1},...,N-1.$

Adopted the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis of this invention, because collecting part K spatial data from actual magnetic resonance equipment at first, its phase encoding scope is :-N/16～N/2-1 (N is the phase encoding number of complete K spatial data), then press the magnetic resonance image (MRI) mathematical model and the multiple singular spectrum analysis model of complex coefficient weighting singular function, the model parameter estimation of carrying out from the Partial K data message, result according to model parameter estimation carries out the magnetic resonance complex image reconstruction by this multiple singular spectrum analysis model at last, thereby guaranteeing under signal noise ratio (snr) of image resolution and the degree of accuracy condition, save sweep time, realized fast imaging; And the Partial K spatial data image reconstructing method of the prior art of comparing, can effectively reduce image error, accurately show former magnetic resonance image (MRI), for detecting, the medical nmr imaging provides high-quality reliable image information; Simultaneously, method highly effective of the present invention, stable and reliable working performance, the scope of application are comparatively extensive, bring great convenience for people's work and life, and have also established solid theories and practical basis for further developing with popularization and application on a large scale of medical imaging detection technique.

Description of drawings

Fig. 1 is the course of work principle schematic based on the magnetic resonant part K image reconstruction data method of answering singular spectrum analysis of the present invention.

Fig. 2 a, 2b are respectively 512 * 512 standard phase images and the master die image of complete K data Fuli leaf inverse transformation in the object simulation magnetic resonance imaging test.

Fig. 2 c, 2d are respectively phase image and the mould image that uses after HM method of the prior art is reconstructed the image of Fig. 2 a, 2b.

Fig. 2 e, 2f are respectively phase image and the mould image that uses after multiple singular spectrum analysis (CSSA) method of the present invention is rebuild the image of Fig. 2 a, 2b.

Fig. 3 a is that the 384th row grey scale curve of Fig. 2 d and Fig. 2 b compares synoptic diagram.

Fig. 3 b is that the 384th row grey scale curve of Fig. 2 f and Fig. 2 b compares synoptic diagram.

Fig. 4 a is the scatter diagram of Fig. 2 d with respect to Fig. 2 b.

Fig. 4 b is the scatter diagram of Fig. 2 f with respect to Fig. 2 b.

Fig. 4 c is the scatter diagram of Fig. 2 c with respect to Fig. 2 a.

Fig. 4 d is the scatter diagram of Fig. 2 e with respect to Fig. 2 a.

Fig. 5 a, 5b are respectively 256 * 256 standard phase images and the master die image of complete K data Fuli leaf inverse transformation in the actual human body magnetic resonance imaging test.

Fig. 5 c, 5d are respectively phase image and the mould image that uses after HM method of the prior art is reconstructed the image of Fig. 5 a, 5b.

Fig. 5 e, 5f are respectively phase image and the mould image that uses after multiple singular spectrum analysis (CSSA) method of the present invention is rebuild the image of Fig. 5 a, 5b.

Fig. 6 a is that the 132nd row grey scale curve of Fig. 5 d and Fig. 5 b compares synoptic diagram.

Fig. 6 b is that the 132nd row grey scale curve of Fig. 5 f and Fig. 5 b compares synoptic diagram.

Fig. 7 a is the scatter diagram of Fig. 5 d with respect to Fig. 5 b.

Fig. 7 b is the scatter diagram of Fig. 5 f with respect to Fig. 5 b.

Fig. 7 c is the scatter diagram of Fig. 5 c with respect to Fig. 5 a.

Fig. 7 d is the scatter diagram of Fig. 5 e with respect to Fig. 5 a.

Embodiment

In order more to be expressly understood technology contents of the present invention, describe in detail especially exemplified by following examples.

The present invention is collecting part K data from actual magnetic resonance equipment, and its phase encoding model is-N/16～N/2-1 that wherein N is the phase encoding number of complete K spatial data.Thereby claim the multiple direct reconstruct magnetic resonance image (MRI) of the singular spectrum analysis method method of utilization to be multiple singular spectrum analysis method (CSSA, Complex Singular Spectrum Analysis).

Before setting forth overall work process of the present invention and principle of work,, at first need to provide to give a definition for clearer and more definite its art-recognized meanings:

Definition 1: a given real or multiple digital signal, the non-vanishing point of its difference is a singular point, and the difference value on the singular point is a singular value, and singular value can be that real number also can be a plural number.

Definition 2: real digital signal w (x), x=0,1 ..., N-1 has a unique singular point, and singular value is 1, claims that then w (x) is a singular function.

If complex digital signal g (x), x=0,1 ..., Q singular point { b arranged on the N-1 ₁, b ₂..., b _Q, then complex digital signal g (x) can be by Q singular function { w _B1(x), w _B2(x) ..., w _BQ(x) } compound linear functional is represented:

$g\left(x\right)=\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{a}_q{w}_{b_q}\left(x\right),x=\mathrm{0,1},...,N-1...\left(1\right)$

Wherein, a ₁, a ₂..., a _QBe Q singular point { b ₁, b ₂..., b _QOn multiple singular value.

With DFT () expression discrete fourier transform operator, then g (x) and w _Bq(x) fourier transform is designated as respectively:

G(k)＝DFT(g(x)) ......(2)

$W_{b_q}\left(k\right)=\mathrm{DFT}\left(w_{b_q}\left(x\right)\right),b_q=\mathrm{0,1},...,Q...\left(3\right)$

Then by formula (1), the fourier transform of g (x) can be expressed as:

$G\left(k\right)=\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{a}_q{W}_{b_q}\left(k\right),k=\mathrm{0,1},...,N-1...\left(4\right)$

As long as any one-row pixels value of magnetic resonance image (MRI) is regarded as an one dimension complex signal g (x), x=0,1 ..., N-1, then the linear functional of the just available multiple singular function of image is represented.

Next step is the estimation to model parameter.If only know the Partial K data, and do not know real image, directly singular point and the singular value that obtains with method of difference is impossible.But can carry out Fuli's leaf inverse transformation to the disappearance part zero padding of Partial K data, obtain approximate image.Thereby can utilize this approximate image, estimate singular point, determine genuine singular point and multiple singular value by the method for separating multiple singular spectrum system of equations then.

If signal g (x), x=0,1 ..., the Fourier spectrum data of N-1 are: G (k), and k=-N/2-1 ..., N/2-1, then the Fourier spectrum data can be expressed as after the missing data zero padding:

G _z(k)＝G(k)R _s-e(k) ......(5)

R wherein _S-e(k) be rectangular function, be defined as follows:

Wherein, s is for blocking upper limiting frequency, and e is for blocking lower frequency limit.

Be used to estimate that the signal of phase place can be expressed as:

g _z(x)＝DFT ^-1(G _z(k))

＝DFT ^-1(G(k)R(k)) ....(7)

＝DFT ^-1(G(k))DFT ^-1(R(k))

＝g(x)r(x)

DFT wherein ^-1The discrete Fuli's leaf inverse transformation operator of () expression,  represents convolution, r (x)=DFT ^-1(R (k)) is:

$r\left(x\right)=\underset{k=s}{\overset{e-1}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="e\; i"\; filenames="A20071003988100182.png,A20071003988100183.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{i}{}},i=\sqrt{-1},x=\mathrm{0,1},...,N-1...\left(8\right)$

Can prove that according to mathematical theory the deconvolution of formula (7) generally can not accurately be calculated, can't ask for g (x) with deconvolution.

For this reason, need to investigate difference:

$d_z\left(x\right)=g_z\left(x\right)-g_z(x-1)$

$={\mathrm{DFT}}^{-1}\left(\right[1-e^{-\frac{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20071003988100182.png,A20071003988100183.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;k}}{N}}\left]G_z\left(k\right)\right)$

$={\mathrm{DFT}}^{-1}\left(\right[1-e^{-\frac{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20071003988100182.png,A20071003988100183.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;k}}{N}}\left]G\left(k\right)R\left(k\right)\right)$

$={\mathrm{DFT}}^{-1}\left(\right[1-e^{-\frac{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20071003988100182.png,A20071003988100183.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;k}}{N}}\left]G\left(k\right)\right)\&CircleTimes;{\mathrm{DFT}}^{-1}\left(R\left(k\right)\right)$

$=[g\left(x\right)-g(x-1)]\&CircleTimes;r\left(x\right)$ .....(9)

Following formula shows g (x), x=0, and 1 ..., the differential signal of N-1 is subjected to the convolution of r (x) and pollutes, and its influence shows as:

(1) the singular point position may drift about;

(2) the false positive singular point may occur in a large number;

(3) the singular value size changes.

If rectangular function R _S-e(k) width is L=e-s, and promptly known frequency spectrum is { G (k ₁), G (k ₂) ..., G (k _L), then can be d _z(x) mould is by arranging from big to small, and L point is as the unusual point set { b of preliminary election before getting ₁, b ₂..., b _L, and structure singular spectrum equation:

The definition matrix:

Then separate into:

a＝W ⁺G ......(11)

W wherein ⁺=(W ^TW) ^-1W ^TThe pseudo inverse matrix of expression W, W ^TThe associate matrix of expression W, (W ^TW) ^-1Expression W ^TThe inverse matrix of W.No matter above-mentioned equation is overdetermination or owes fixed, can obtain a least error with the pseudo inverse matrix method and separate, obtain L plural singular value { a ₁, a ₂..., a _L.

At this moment, if a _i=0,0＜i≤L, then b _i, 0＜i≤L is called the false positive singular point.Because a _i=0, by above-mentioned formula (1) reconstruct complex digital signal or by above-mentioned formula (4) reconstruct Fourier spectrum data, false positive is unusual just can not to influence reconstruction result.

See also shown in Figure 1ly, the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis of the present invention may further comprise the steps:

(1) collecting part K data G (k) from magnetic resonance equipment, its phase encoding scope can be-N/16～N/2-1, wherein N is the phase encoding number of complete K spatial data;

(2) set up the mathematical model and the multiple singular spectrum analysis model of the magnetic resonance image (MRI) of complex coefficient weighting singular function for these Partial K data; Wherein, the magnetic resonance image (MRI) mathematical model of the complex coefficient weighting singular function of foundation is:

$g\left(x\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{w}_{b_q}\left(x\right),x=\mathrm{0,1},...,N-1;$

Wherein, g (x), x=0,1 ..., N-1 is a complex digital signal, { b ₁, b ₂..., b _QBe Q singular point on the g (x), { w _B1(x), w _B2(x) ..., w _BQ(x) } for respectively with { b ₁, b ₂..., b _QBe Q singular function of singular point, a ₁, a ₂..., a _QBe this Q singular point { b ₁, b ₂..., b _QOn multiple singular value.

The multiple singular spectrum analysis model of setting up is:

$G\left(k\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{W}_{b_q}\left(k\right),k=\mathrm{0,1},...,N-1;$

Wherein, G (k)=DFT (g (x)), $W_{b_q}\left(k\right)=\mathrm{DFT}\left(w_{b_q}\left(x\right)\right),$ b _q=0,1 ..., Q, DFT () they are the discrete fourier transform operator;

(3) utilize the mathematical model and the multiple singular spectrum analysis model of described magnetic resonance image (MRI), carry out model parameter estimation, may further comprise the steps according to this Partial K data message:

(a), and obtain Fourier spectrum data G after the missing data zero padding according to following formula to the disappearance part zero padding of these Partial K data G (k) _z(k):

G _z(k)＝G(k)R _s-e(k)；

Wherein, G (k) is signal g (x), x=0, and 1 ..., the Fourier spectrum data of N-1, k=-N/2-1 ..., N/2-1, Be rectangular function, wherein s is for blocking upper limiting frequency, and e is for blocking lower frequency limit;

(b) calculate d according to following formula _z(x):

d _z(x)＝g _z(x)-g _z(x-1)；

Wherein, g _z(x)=DFT ^-1(G _z(k)), k=-N/2-1 ..., N/2-1, DFT ^-1The discrete Fuli's leaf inverse transformation operator of () expression;

(c) with resulting d _z(x) mould is according to ordering from big to small, and before getting L put as the unusual point set { b of preliminary election ₁, b ₂..., b _L, wherein L is rectangular function R _S-e(k) width, i.e. L=e-s, and known frequency spectrum are { G (k ₁), G (k ₂) ..., G (k _L);

(d) according to following formula construction singular spectrum equation:

(e) solve described singular spectrum equation with the pseudo inverse matrix method, obtain a least error and separate, obtain L plural singular value { a ₁, a ₂..., a _L;

(f) with { a ₁, a ₂..., a _LReturn as the result of model parameter estimation;

(4) according to the result of model parameter estimation, utilize the mathematical model of described magnetic resonance image (MRI) and multiple singular spectrum analysis model to carry out the reconstruct of magnetic resonance complex pattern, be specially:

Can be based on the result { a of model parameter estimation ₁, a ₂..., a _L, according to the described complex digital signal g of following formula reconstruct (x):

$g\left(x\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{w}_{b_q}\left(x\right),x=\mathrm{0,1},...,N-1;$

Perhaps, also can be based on the result { a of model parameter estimation ₁, a ₂..., a _L, according to following formula reconstruct described Fourier spectrum data G (k):

$G\left(k\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{W}_{b_q}\left(k\right),k=\mathrm{0,1},...,N-1.$

Below with Fuli's leaf contravariant die change image of complete K spatial data and phase image as the reference standard, to same phase encoding model be-the Partial K data of N/16～N/2-1, be reconstructed gained phase image and mould image with CSSA and HM algorithm respectively, carry out the comparison of image, diffusing point (scatter) figure and sectional view (Profile Line) then with standard picture.

See also shown in Fig. 2 a～2f, it compares for image reconstruction algorithm in the object simulation magnetic resonance imaging test, Fig. 2 a and 2b are respectively the standard phase image and the master die image of complete K data Fuli leaf inverse transformation, Fig. 2 c and 2d are respectively phase image and the mould images of Partial K data with the reconstruct of HM method, and Fig. 2 e and 2f are respectively phase image and the mould images of Partial K data with the reconstruct of CSSA method.

From phase image, Fig. 2 c has a large amount of artefacts, differs bigger with standard picture Fig. 2 a, because Fig. 2 c and Fig. 2 a are quite approaching, so that is difficult to identification at first view.From phase image, as can be seen, details resolution aspect CSSA and HM can both satisfy the actual clinical requirement in similar result on the grid of image, but Fig. 2 d with the naked eye just can observe the large stretch of subregion that has obvious distortion for Fig. 2 b, does not then have this phenomenon among Fig. 2 f.And generally, this distortion phenomenon is enough to make the clinical diagnosis doctor to produce mistaken diagnosis.

See also again shown in Fig. 3 a, the 3b, wherein Fig. 3 a is the 384th capable grey scale curve comparison synoptic diagram of Fig. 2 d and Fig. 2 b, Fig. 3 b is that the grey scale curve of the 384th row of Fig. 2 f and Fig. 2 b compares synoptic diagram, can know from Fig. 3 a and see that the HM method has bigger error that Fig. 3 b then two curves presses close to very much.

See also shown in Fig. 4 a～4d, wherein Fig. 4 a and 4b are respectively HM and CSSA phase image of the present invention scatter diagrams to standard phase image Fig. 2 b again.Scatter diagram (Scatter Figure) is analyzed the difference of two algorithms on reconstruction accuracy with can being used for sxemiquantitative.Scatter diagram is that two pixel values of two width of cloth images on same coordinate are the diffusing point coordinate of some picture that looses, and draws a little on this diffusing point coordinate, thereby constitutes scatter diagram.If it is just the same that two width of cloth images have, the coordinate in length and breadth of drawing point must equate, thereby the point that looses only is distributed on 45 ° of diagonal line, represents the closer to 45 ° of diagonal line that two images approached more at diffusing o'clock of scatter diagram.Line chart is that the gray scale of getting on a certain row or column of image draws (we are called line chart) with the change in location curve, can further find the difference on HM method and the CSSA reconstruction accuracy easily.

Simultaneously, the phase place scatter diagram is the phase place of image under consideration background not, because background phase is unordered, and to the not influence of restructuring graph picture element amount.From the scatter diagram of Fig. 4 a and 4b Comparatively speaking, the error of Fig. 4 b will be much smaller than Fig. 4 a, thereby has illustrated that CSSA method of the present invention will outclass the HM method.Fig. 4 c and 4d are respectively HM and CSSA mould image of the present invention scatter diagrams to the master die image.From the phase place scatter diagram of Fig. 4 c and 4d Comparatively speaking, the error of Fig. 4 d will be much smaller than Fig. 4 c, and Fig. 4 c is expansion trend in high pixel value district, illustrated that the HM reconstructing method is not than mistake at background area yet, and the scatter diagram of Fig. 4 d is illustrated in the error range of image-region within the noise scope, thereby proved that CSSA method of the present invention is a kind of method of practicality, and the relative unreliability of HM method.

See also again shown in Fig. 5 a～5f, be the actual magnetic resonance image-forming in the actual human body magnetic resonance imaging test, T1 MPR3DSAG 1mm, visual field height=350mm, wide=263mm, length=350mm, TR=1.97s, TE=4.69ms, image resolution ratio 176 * 256 * 256, wherein Fig. 5 a, 5b are respectively the 88th K data of taking out in the test are used the reconstruction of Fuli's leaf inverse transformation as complete K data standard phase image and master die image.And, use HM and CSSA method reconstructed phase image and mould image respectively with the K data of wherein-16～128 phase encodings Partial K data as experiment.In the reconstructed results, Fig. 5 c, 5d are respectively from the phase image of HM reconstruct and mould image, all phase image and the mould image difference with standard is bigger for it, especially image central authorities also have showy bright of lattice, this is due to the HM reconstructed error, and Fig. 5 e, 5f are respectively the phase image and the mould image of CSSA method of the present invention reconstruct, and it looks and original image is a basically identical.

Fig. 6 a is the 132nd row grey scale curve figure of Fig. 5 d and Fig. 5 b, and Fig. 6 b is the grey scale curve figure of the 132nd row of Fig. 5 f and Fig. 5 b, can know from Fig. 6 a and see that the HM method has bigger error, and Fig. 6 b then two grey scale curve presses close to very much.

Fig. 7 a, 7b are respectively the actual magnetic resonance K data scatter diagrams (not image under consideration background phase) of the phase image of HM and the reconstruct of CSSA method to the standard phase image.The phase place scatter diagram of Fig. 7 a, 7b Comparatively speaking, the error of Fig. 7 b will illustrate that also CSSA method of the present invention will outclass the image of HM method reconstruct much smaller than Fig. 7 a.Fig. 7 c and 7d are respectively HM and the CSSA mould image scatter diagrams to the master die image.Mould scatter diagram according to Fig. 7 c and 7d, the error of finding Fig. 7 d will be much smaller than Fig. 7 c, and Fig. 7 c is expansion trend at high gray area, illustrated in actual K data imaging, the image of HM method reconstruct is also bigger in the error of image-region, surpass the noise fluctuations scope, Fig. 7 d is then different, and it still is within the noise normal range that is allowed.The experimental result of the image reconstruction of actual magnetic resonance K data is model magnetic resonant part K data experiment unanimity as a result also, show that the CSSA method is a kind of method of practicality, and the HM method has certain unreliability.

Simultaneously, the principal feature of CSSA method reconstructed image of the present invention is that it has utilized the Partial K data to comprise the characteristics of missing data information, and utilization zero padding imaging, difference and the multiple singular function magnetic resonance image (MRI) model parameter of multiple singular spectrum analysis method extraction, the multiple singular function magnetic resonance image (MRI) model of utilization reconstructs the image of complete K data correspondence again.And by contrast, the HM method error not only is on the error of phase estimation, also is on its algorithm principle.Even the HM method also can not obtain accurate magnetic resonance image (MRI) under the right-on prerequisite of phase estimation, removing non-image is equiphase magnetic resonance image (MRI).

Moreover, feature based on the magnetic resonant part K image reconstruction data method of answering singular spectrum analysis of the present invention is that also it is to have utilized the Partial K data to comprise the characteristics of missing data information, do not need to carry out phase estimation and phase correction, thereby walked around the phase estimation problem dexterously.Its utilization zero padding image is estimated, difference reaches multiple singular spectrum analysis method and extracts multiple singular function magnetic resonance image (MRI) model parameter, the multiple singular function magnetic resonance image (MRI) model of utilization reconstructs the image of complete K data correspondence again, thereby has warded off a high precision Partial K data magnetic resonance image (MRI) method for reconstructing in addition.Phase image and mould image from the test of above object simulation test and actual human body, can both be very clear and definite show that its steady quality can reach the clinical medicine application level with CSSA method of the present invention reconstruct Partial K accurately data image.

Adopted above-mentioned magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis, owing at first from actual magnetic resonance equipment, collect the Partial K data of phase encoding scope-N/16～N/2-1 (N is the phase encoding number of complete K spatial data), from the model parameter estimation of carrying out of Partial K data message, the result according to model parameter estimation carries out the magnetic resonance complex image reconstruction by this multiple singular spectrum analysis model at last then.Adopt the magnetic resonant part K image reconstruction data method of this kind based on multiple singular spectrum analysis, guaranteeing under signal noise ratio (snr) of image resolution and the degree of accuracy condition, save sweep time, realize fast imaging, provide high-quality reliable image information for the medical nmr imaging detects; More existing Partial K spatial data image reconstructing method can effectively reduce image error, accurately shows former magnetic resonance image (MRI), provides high-quality reliable image information for the medical nmr imaging detects; Simultaneously, method highly effective of the present invention, stable and reliable working performance, the scope of application are comparatively extensive, bring great convenience for people's work and life, and have also established solid theories and practical basis for further developing with popularization and application on a large scale of medical imaging detection technique.

In this instructions, the present invention is described with reference to its certain embodiments.But, still can make various modifications and conversion obviously and not deviate from the spirit and scope of the present invention.Therefore, instructions and accompanying drawing are regarded in an illustrative, rather than a restrictive.

Claims (6)

1, a kind of magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis is characterized in that described method may further comprise the steps:

(1) collecting part K data G (k) in the phase encoding scope of from magnetic resonance imagine scanner, presetting;

(2) carry out model parameter estimation according to this Partial K data message;

(3), utilize the mathematical model and the multiple singular spectrum analysis model of the magnetic resonance image (MRI) of complex coefficient weighting singular function to carry out the reconstruct of magnetic resonance complex pattern according to the result of model parameter estimation.

2, the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis according to claim 1 is characterized in that, the phase encoding scope of described systemic presupposition is-N/16～N/2-1, and wherein N is the phase encoding number of complete K spatial data.

3, the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis according to claim 1 is characterized in that the magnetic resonance image (MRI) mathematical model of described complex coefficient weighting singular function is:

$g\left(x\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{w}_{b_q}\left(x\right),x=\mathrm{0,1},...,N-1;$

Wherein, g (x), x=0,1 ..., N-1 is a complex digital signal, { b ₁, b ₂..., b _QBe Q singular point on the g (x), { w _B1(x), w _B2(x) ..., w _BQ(x) } for respectively with { b ₁, b ₂..., b _QBe Q singular function of singular point, a ₁, a ₂..., a _QBe this Q singular point { b ₁, b ₂..., b _QOn multiple singular value.

4, the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis according to claim 3 is characterized in that, described multiple singular spectrum analysis model is:

$G\left(k\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{W}_{b_q}\left(k\right),k=\mathrm{0,1},...,N-1;$

Wherein, G (k)=DFT (g (x)), $W_{b_q}\left(k\right)=\mathrm{DFT}\left(w_{b_q}\left(x\right)\right),$ Q=0,1 ..., Q, DFT () they are the discrete fourier transform operator.

5, the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis according to claim 4 is characterized in that the described model parameter estimation of carrying out may further comprise the steps:

(1), and obtains Fourier spectrum data G after the missing data zero padding according to following formula to the disappearance part zero padding of these Partial K data G (k) _z(k):

G _z(k)＝G(k)R _s-e(k)；

Wherein, G (k) is signal g (x), x=0, and 1 ..., the Fourier spectrum data of N-1, k=-N/2-1 ..., N/2-1,

Be rectangular function, wherein s is for blocking upper limiting frequency, and e is for blocking lower frequency limit;

(2) calculate d according to following formula _z(x):

d _z(x)＝g _z(x)-g _z(x-1)；

Wherein, g _z(x)=DFT ^-1(G _z(k)), k=-N/2-1 ..., N/2-1, DFT ^-1The discrete Fuli's leaf inverse transformation operator of () expression;

(3) with resulting d _z(x) mould is according to ordering from big to small, and before getting L put as the unusual point set { b of preliminary election ₁, b ₂..., b _L, wherein L is rectangular function R _S-e(k) width, i.e. L=e-s, and known frequency spectrum are { G (k ₁), G (k ₂) ..., G (k _L);

(4) according to following formula construction singular spectrum equation:

(5) solve described singular spectrum equation with the pseudo inverse matrix method, obtain a least error and separate, obtain L plural singular value { a ₁, a ₂..., a _L;

(6) with { a ₁, a ₂..., a _LReturn as the result of model parameter estimation.

6, the magnetic resonant part K image reconstruction data method based on multiple singular spectrum analysis according to claim 5 is characterized in that, describedly carries out being reconstructed into of magnetic resonance complex pattern:

Result { a based on model parameter estimation ₁, a ₂..., a _L, according to the described complex digital signal g of following formula reconstruct (x):

$g\left(x\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{w}_{b_q}\left(x\right),x=\mathrm{0,1},...,N-1;$

Perhaps, based on the result { a of model parameter estimation ₁, a ₂..., a _L, according to following formula reconstruct described Fourier spectrum data G (k):

$G\left(k\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}{a}_q{W}_{b_q}\left(k\right),k=\mathrm{0,1},...,N-1.$

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