CN102779327A - Water and fat separation method based on under-sampling k-space data - Google Patents

Water and fat separation method based on under-sampling k-space data Download PDF

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CN102779327A
CN102779327A CN2011101219883A CN201110121988A CN102779327A CN 102779327 A CN102779327 A CN 102779327A CN 2011101219883 A CN2011101219883 A CN 2011101219883A CN 201110121988 A CN201110121988 A CN 201110121988A CN 102779327 A CN102779327 A CN 102779327A
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CN102779327B (en
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张强
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Shenzhen Union Medical Technology Co., Ltd.
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Shanghai United Imaging Healthcare Co Ltd
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Abstract

The invention discloses a water and fat separation method based on under-sampling k-space data. The method includes steps of, step one, respectively acquiring k-space trajectory parameters and k-space raw data according to magnetic resonance (MR) raw data; step two, selecting a parameter system matrix according to the k-space trajectory parameters; step three, acquiring echo data of each channel according to the k-space raw data; step four, executing regularization iteration image reconstruction by using the parameter system matrix and the echo data of each channel; and step five, subjecting reconstructed images to variable projection (VARPRO) water and fat separation calculating to obtain a final image. The water and fat separation method based on the under-sampling k-space data is applicable to more scanning tracks, and by means of a VARPRO water and fat separation algorithm, a phase diagram, a B0 field image, a water image and a fat image which are irrelevant to main magnetic field inhomogeneity are separated; the water and fat separation method based on the under-sampling k-space data has advantages of VARPRO iteration field image calculating and is insensitive to seed points; and the water and fat separation method based on the under-sampling k-space data is smaller in calculated amount and fewer in calculating requirements, image merging is easier to finish, and a system function which is capable of achieving parallel imaging can be introduced.

Description

A kind of water fat separation method based on the k-spatial data of owing to sample
Technical field
The invention belongs to field of medical image processing, relate to a kind of water fat separation method based on the k-spatial data of owing to sample.
Background technology
In Magnetic resonance imaging, because the existence of local non homogen field, conventional fat suppression method, water exciting method and short inversion recovery (STIR) can suppress the fat failure in these zones, thereby cause some pathologic structure to be hidden by the fat signal of Gao Liang.Multiple spot Dixon method based on the chemical shift of water fat has better robustness under this condition.Conventional multiple spot Dixon method is based on that the data of filling in Descartes k-space rebuild, and the collection of these data normally combines spin echo, FSE, and gtadient echos etc. obtain.This method need be done complete k-space usually and fill to avoid occurring owing to sample pseudo-shadow, and sweep time is long.Simultaneously this Descartes's filling mode for patient move, motion sensitive such as pulse, can produce pseudo-shadow at the phase-encoding direction of image.Someone proposes to owe sampling with the shortening time to the k-space; And combine for the comparatively insensitive k-of motion space fill pattern; Fill pattern like radial or PROPELLOR; Then the imagery exploitation lattice point method or the iterative reconstruction approach of each echo are rebuild, the B0 field pattern analytical approach that increases with conventional multiple spot water fat separation method calmodulin binding domain CaM is at last obtained water picture and fat picture.This method can shorten sweep time and obtain reasonable image, but the region growing method has certain instability and need expend bigger computer resource, probably causes local water fat to separate failure.
Summary of the invention
Technical matters to be solved by this invention is: a kind of water fat separation method of the k-spatial data of owing to sample is provided, and this method can be isolated and the incoherent phase diagram of main field unevenness, B0 field pattern and water picture and fat picture.
For solving the problems of the technologies described above, the present invention adopts following technical scheme.
A kind of water fat separation method based on the k-spatial data of owing to sample may further comprise the steps:
Step 1 is obtained k-space tracking parameter and k-space raw data respectively according to the MR raw data;
Step 2 is according to said k-space tracking selection of parameter parameter system matrix;
Step 3 is obtained the echo data of each passage according to said k-space raw data;
Step 4 utilizes the echo data of said parameter system matrix and each passage to carry out the regularization iterative image reconstruction;
Step 5 is carried out VARPRO water fat decouples computation with the image after rebuilding, and obtains final image.
As a kind of preferred version of the present invention, in the step 5, the image after will rebuilding earlier carries out VARPRO water fat decouples computation, will carry out image through the image after water fat separates then and merge, and obtains final image at last.
As another kind of preferred version of the present invention, in the step 5, the image after will rebuilding earlier carries out image and merges, and then the image after will merging carries out VARPRO water fat decouples computation, obtains final image at last.
As another preferred version of the present invention, in the step 4, the method for said regularization iterative image reconstruction may further comprise the steps:
1) estimates initial pictures;
2) estimate present image;
3) confirm the direction of search;
4) carry out line search to upgrade step-length according to system matrix, MR raw data and the direction of search;
5) update image;
6) upgrade the direction of search;
7) judge whether to satisfy inner iteration and stop criterion, then do not return step 4) if do not satisfy; Then continue execution in step 8 if satisfy);
8) image after estimation improves;
9) judge whether to reach the greatest iteration step number of setting, if reach then execution in step 10); Otherwise judge whether to satisfy outside iteration and stop criterion, if satisfy then execution in step 10), otherwise return step 2);
10) output final image;
As another preferred version of the present invention, in the step 5, said VARPRO water fat decouples computation may further comprise the steps:
The 1st step, initial field pattern are estimated, are set to matrix
Figure BDA0000060671690000021
The 2nd the step, to one group of inhomogeneous value
Figure BDA0000060671690000022
to all pixel precomputation cost functions
Figure BDA0000060671690000023
wherein
Figure BDA0000060671690000024
be the field unevenness lower limit;
Figure BDA0000060671690000025
is the upper limit of a unevenness, and scope
Figure BDA0000060671690000026
is split into L point;
Figure BDA0000060671690000027
representes l point; It is l ∈ [1, L];
The 3rd the step, for each the pixel q in the image by formula
Figure BDA0000060671690000028
The estimation of renewal field pattern, wherein δ qJ * the J that is pixel q faces the territory, and μ is the weight of the smoothing factor total amount of control Markov random field introducing,
Figure BDA0000060671690000031
Be the field unevenness of pixel q,
Figure BDA0000060671690000032
The field unevenness currency of remarked pixel j, The new field unevenness estimated value of remarked pixel q, W Q, jThe weight factor of difference between expression control pixel q and the j; The 4th step, the 3rd step of repetition change less than threshold xi until total field pattern, ξ＞0, promptly
Figure BDA0000060671690000034
Wherein, Q representes the total pixel number of field pattern,
Figure BDA0000060671690000035
The field unevenness currency of remarked pixel q;
The 5th step, basis
Figure BDA0000060671690000036
Calculate phase place
Figure BDA0000060671690000037
S -τAnd S + τFor at the TE/2-τ of normal TE/2 echo both sides and the signal at TE/2+ τ place;
The 6th the step, for each pixel in the image, by formula
Figure BDA0000060671690000038
In conjunction with
Figure BDA0000060671690000039
With
Figure BDA00000606716900000310
Calculate ρ wAnd ρ fWherein
Figure BDA00000606716900000311
ψ +Be the pseudo inverse matrix of ψ, I is N * N unit matrix,
Figure BDA00000606716900000313
The final output of expression field pattern,
Figure BDA00000606716900000314
Expression field pattern function,
Figure BDA00000606716900000315
Expression water and fatty density picture,
Figure BDA00000606716900000316
For with f B0Signal cost function for variable; t 1, t 2... T MThe expression signal echo time;
Figure BDA00000606716900000317
The set of signals that the different echo times of expression obtain, ρ wBe expressed as the signal intensity of water constituent, ρ fThe signal intensity of expression fat constituent.
As another preferred version of the present invention, in the step 1, said MR raw data is on the MR scanner, to fill track by sequence of setting and k-space to obtain.
As another preferred version of the present invention, in the step 2, said system matrix is non-homogeneous FFT system matrix and the inverse operation matrix that generates according to k-space tracking parameter.
Beneficial effect of the present invention is: the track while scan that the method for the invention is suitable for is more, and it adopts the separation algorithm of VARPRO, can isolate and the incoherent phase diagram of main field unevenness, B0 field pattern and water picture and fat picture; Also utilize VARPRO not adopt the characteristic of region growing method, inherited the advantage of the iteration field pattern calculating of VARPOR, need not choose seed points, insensitive to seed points; And calculated amount and computation requirement are lower, are easier to accomplish the system function that image merges and introduces parallel imaging.
Description of drawings
Fig. 1 is the pulse train synoptic diagram of FSE;
Fig. 2 is opportunity of the present invention owe the to sample schematic flow sheet of water fat separation method of k-spatial data;
Fig. 3 is the schematic flow sheet of embodiment two described water fat separation methods;
Fig. 4 is the schematic flow sheet of regularization Iteration Image Reconstruction Algorithm;
Fig. 5 is the schematic flow sheet of VARPRO water fat separation algorithm.
Embodiment
Do further explain below in conjunction with the accompanying drawing specific embodiments of the invention.
Embodiment one
Present embodiment provides a kind of water fat separation method of the k-spatial data of owing to sample, and concrete implementation procedure is following:
FSE abbreviates FSE (Fast Spin Echo) or Turbo SE (TSE) as.In common SE sequence, at first launch 90 ° of RF pulses in the cycle at a TR, launch 180 ° of RF pulses then, form a spin echo.The FSE sequence is the same with many echo sequences, also is at first to launch 90 ° of RF pulses in the cycle at a TR, and a plurality of 180 ° of RF pulses of sequential transmissions then form a plurality of spin echoes.But the two is essentially different.In many echoes SE sequence; Each TR cycle obtains specific phase encoding data, and promptly phase gradient scans with same intensity among each TR, and the data of collection are only filled the delegation in k-space; Each echo participates in producing piece image, finally can obtain the image of several different weights.And in the FSE sequence, obtain a plurality of different phase coded datas independent of each other in each TR time, and promptly forming the desired phase gradient of each echo to vary in size, the data of collection can be filled several row in k-space, and final one group of echo combines to form piece image.Because a TR cycle obtains a plurality of phase encoding data, can use the less TR cycle to form piece image, thereby shorten sweep time.
Fig. 1 has shown that the multiple spot Dixon based on fast acquisition interleaved spin echo gathers, and as shown in the figure, the multiple spot Dixon that touches upon among the present invention gathers and refers to after reunion RF pulse; It is a plurality of echo acquirements of τ in front and back, normal echo TE/2 position with the adjacent time interval with reunion gradient mutually mutually that employing is loose in advance, i.e. time interval set is TE/2-k τ, TE/2-(k-1) τ; TE/2-τ, TE/2, TE/2+ τ;, TE/2+ (h-1) τ, TE/2+h τ; The wherein symmetry decision that had of the echo number that obtains by needs of the setting of k and h and normal relatively echo TE.Through phase encoding gradient (GPE) the two-dimentional k-space tracking different with being combined to form of frequency coding gradient (GRO); Like spiral (spiral); Actinomorphic (radial), and PROPELLOR (the parallel phase encoding line collection that rotates at interval with equal angles around k space center) etc.For the RF pulse of once meeting again together, phase encoding gradient is consistent, therefore for different echoes, in the data of gathering after same reunion RF pulse position consistency in the k-space of filling separately.As shown in Figure 1, each 180 ° return gather pulse after, the several echoes of continuous acquisition; Wherein time interval is that 180 ° echo is a spin echo, is defined as k0, and other several echoes appear at the front and back of spin echo with same intervals τ; Promptly be defined as k-1, k-2, k1; K2 ..., that is to say that the corresponding echo time of these echoes does
t m＝mτ+TE/2，m＝-2，-1，0，1，2，…
Wherein, m representes the position of echo; As required, can move the position of these echoes, as-1,0,1,2,3 etc.As describing among Fig. 1, TE/2 is the time of reunion RF pulse to normal echo position; Simple in order to describe, the position of echo can be expressed as s 1, s 2..., s m, m ∈ [1, M], M confirm by the echo quantity that algorithm needs, for example during 3 Dixon, and M=3.According to these echo times, corresponding water fat chemical shift encoding phase does
Figure BDA0000060671690000051
f WfIt is the fat frequency shifts of water relatively.Because the unevenness of local field, image/signal that the different time echo obtains does
Figure BDA0000060671690000052
Wherein Be and the irrelevant introducing phase error of main field, for example come from the space phase distributional difference between each receiving coil, this species diversity and time integral are irrelevant, and relative fixed, can be relatively easy to from the image of a plurality of echoed signals, separate; ρ wBe the signal intensity of water constituent, ρ fBe the signal intensity of fat constituent, γ is gyromagnetic ratio (is 42.5756MHz/T for proton), Δ B 0Be the field unevenness; Can the view data of all echoes be collected into vector by acquisition order
s → = ( s 1 , s 2 , · · · , s e ) - - - ( 3 )
The data in k-space can be expressed as
Figure BDA0000060671690000055
F is based on the different spaces coding mode, more stresses not exclusively in the present invention or uneven fill pattern, as the radial that owes to sample, PROPELLOR or fill pattern at random etc.
Figure BDA0000060671690000056
is the original k-spatial data that collects.For multiple spot Dixon, the present invention rebuilds each echo earlier, can adopt flow process as shown in Figure 2 to obtain the B0 field pattern, also obtain subsequently water picture and fatty the picture then.For obtaining of image, the present invention has adopted similarly method of VARPRO (Variable Projection, variable projection).
The acquisition process of B0 field pattern is as shown in Figure 2, may further comprise the steps:
Track acquisition raw data (being the MR raw data) is filled in the first step, sequence and k-space by setting on the MR scanner, and each echo that multiple spot Dixon is corresponding is filled in the k-space separately.
Second step, combination imaging sequence and raw data, the k-space tracking parameter that acquisition algorithm needs.
The 3rd goes on foot, obtains from raw data and isolate the corresponding raw data of each echo.And the data of each echo further are decomposed into the data on the corresponding imaging passage and preserve.
The 4th the step, according to second the step in k-space tracking parameter, utilize the kit of FFTW3 and so on to generate non-homogeneous FFT system matrix F and inverse operation matrix F #
The 5th step, the system matrix of raw data and generation is input in the regularization interative computation module.Regularization interative computation module such as Fig. 4 description.Need to prove that present embodiment is only listed a kind of alternative manner, other can be applied to the method for reconstructing owing to sample, and like the alternative manner based on Gauss-Newton, perhaps other algebraic methods also can be used to replace the alternative manner that the present invention mentions.Therefore, the scope of the present invention's covering is the association schemes that iterative approximation separates with VARPRO water fat.This iteration output image is labeled as each pixel of
Figure BDA0000060671690000061
these images and has expressed the signal of describing in the formula (2).
The 6th step, the image that the 5th step was obtained are input to VARPRO water fat decouples computation module acquisition B0 field pattern, water picture and fat picture; In this step; Input can be handled according to the flow process of Fig. 2 from the image
Figure BDA0000060671690000062
of the different echoes of different passages; Concrete disposal route is: A1, utilize the image merge algorithm; Each channel image that each echo is corresponding merges, and merge algorithm can adopt self-adaptation coil merge algorithm; Image after A2, the different echoes of input merge utilizes the method for VARPRO to calculate B0, water picture and fat picture.Wherein, it is as shown in Figure 5 to utilize the method for VARPRO to calculate the method flow of B0, water picture and fatty picture, may further comprise the steps:
At first according to the theory of VARPRO, the formula that extraction algorithm is relevant is following
f B 0 fin = arg mi n f B 0 R ( f B 0 ) = arg min f B 0 | | [ I - Ψ ( f B 0 ) Ψ + ( f B 0 ) ] s → | | 2 2 - - - ( 4 )
ρ fin → = ( ρ w , ρ f ) fin = Ψ + ( f B 0 fin ) s → - - - ( 5 )
Ψ = e i 2 π f B 0 t 1 e i 2 π ( f B 0 + f wf ) t 1 e i 2 π f B 0 t 2 e i 2 π ( f B 0 + f wf ) t 2 · · · · · · e i 2 π f B 0 t M e i 2 π ( f B 0 + f wf ) t M - - - ( 6 )
Wherein, ψ +It is the pseudo inverse matrix of ψ.I is N * N unit matrix.
Figure BDA0000060671690000066
The final output of expression field pattern,
Figure BDA0000060671690000067
Expression field pattern function,
Figure BDA0000060671690000068
Expression expression water and fatty density picture,
Figure BDA0000060671690000069
Be with f B0Signal cost function for variable.
The 1st step, initial field pattern are estimated, are set to matrix
Figure BDA00000606716900000610
The 2nd the step, to one group of inhomogeneous value
Figure BDA00000606716900000611
to all pixel precomputation cost functions
Figure BDA00000606716900000612
wherein
Figure BDA00000606716900000613
be the field unevenness lower limit;
Figure BDA00000606716900000614
is the upper limit of a unevenness, and scope
Figure BDA00000606716900000615
is split into L point;
Figure BDA00000606716900000616
representes l point; It is l ∈ [1, L];
The 3rd the step, for each the pixel q in the image by formula
Figure BDA0000060671690000071
The estimation of renewal field pattern, wherein δ qJ * the J that is pixel q faces the territory, and μ is the weight of the smoothing factor total amount of control Markov random field introducing,
Figure BDA0000060671690000072
Be the field unevenness of pixel q,
Figure BDA0000060671690000073
The field unevenness currency of remarked pixel j,
Figure BDA0000060671690000074
The new field unevenness estimated value of remarked pixel q, W Q, jThe weight factor of difference between expression control pixel q and the j;
The 4th step, the 3rd step of repetition change less than threshold xi until total field pattern; ξ＞0; Promptly
Figure BDA0000060671690000075
wherein; Q representes the total pixel number of field pattern,
Figure BDA0000060671690000076
the field unevenness currency of remarked pixel q;
The 5th step, basis
Figure BDA0000060671690000077
Calculate phase place S -τAnd S + τFor at the TE-τ of normal TE echo both sides and the signal at TE+ τ place;
The 6th the step, for each pixel in the image, by formula In conjunction with
Figure BDA00000606716900000710
With
Figure BDA00000606716900000711
Calculate ρ wAnd ρ fWherein ψ +Be the pseudo inverse matrix of ψ, I is N * N unit matrix,
Figure BDA00000606716900000714
The final output of expression field pattern, Expression field pattern function,
Figure BDA00000606716900000716
Expression water and fatty density picture,
Figure BDA00000606716900000717
For with f B0Signal cost function for variable; t 1, t 2... T MThe expression signal echo time; The set of signals that the different echo times of expression obtain; ρ wBe expressed as the signal intensity of water constituent, ρ fThe signal intensity of expression fat constituent.
Embodiment two
The water fat separation method that present embodiment provides another kind to owe to sample the k-spatial data; The difference of itself and embodiment one is: in the 6th step; Input is handled according to flow process shown in Figure 3 from the image
Figure BDA00000606716900000719
of the different echoes of different passages; Concrete disposal route is: B1, import the image of the different echoes of each imaging passage, utilize the method for VARPRO to calculate the corresponding B0 of each imaging passage, water picture and fat picture; B2, the B0 on the single passage, water picture and fat picture are carried out corresponding merging.
Said scheme of present embodiment and embodiment one said scheme can be complementary implementations.Its selection can be based on signal to noise ratio (S/N ratio) of image etc.For example; The noise level prescan that can gather before the imaging obtains the signal to noise ratio (S/N ratio) of single passage; Perhaps based on the ratio of echo center, k-space and platform; And whether satisfy certain criterion according to this signal to noise ratio (S/N ratio) or ratio, as be higher than and be lower than certain threshold value, embodiment one said scheme or the said scheme of present embodiment selected.
Major technique characteristic of the present invention and originality are to combine the VARPRO water fat separation algorithm of regularized image reconstruction algorithm and improvement, and are applied to the MR raw data of owing to sample.The method of the invention is not subject to concrete imaging sequence, k-space tracking pattern.With respect to the application that He Qiang proposes in Siemens, the present invention has following advantage than traditional water fat separation method that it adopts:
1, the track while scan that is suitable for is more;
2, the present invention adopts the separation algorithm of VARPRO, can isolate and the incoherent phase diagram of main field unevenness (gathering the space phase distributional difference relatively like coil channel), B0 field pattern and water picture and fat picture;
3, the present invention utilizes VARPRO not adopt the characteristic of region growing method, has therefore inherited the advantage of the iteration field pattern calculating of VARPOR, promptly need not choose seed points, and is therefore insensitive to seed points;
4, the compressed sensing iterative reconstruction algorithm that proposes with respect to people such as Mariya based on IDEAL, the flow process of the method for the invention is more clear, and calculated amount and computation requirement are lower, are easier to accomplish the system function that image merges and introduces parallel imaging.
Description of the invention and application are illustrative, are not to want with scope restriction of the present invention in the above-described embodiments.Here the distortion of the embodiment that is disclosed and change are possible, and the replacement of embodiment is known with the various parts of equivalence for those those of ordinary skill in the art.Those skilled in the art are noted that under the situation that does not break away from spirit of the present invention or essential characteristic, and the present invention can be with other forms, structure, layout, ratio, and realize with other elements, material and parts.

Claims (7)

1. the water fat separation method based on the k-spatial data of owing to sample is characterized in that, may further comprise the steps:
Step 1 is obtained k-space tracking parameter and k-space raw data respectively according to the MR raw data;
Step 2 is according to said k-space tracking selection of parameter parameter system matrix;
Step 3 is obtained the echo data of each passage according to said k-space raw data;
Step 4 utilizes the echo data of said parameter system matrix and each passage to carry out the regularization iterative image reconstruction;
Step 5 is carried out VARPRO water fat decouples computation with the image after rebuilding, and obtains final image.
2. the water fat separation method based on the k-spatial data of owing to sample according to claim 1; It is characterized in that: in the step 5; Image after will rebuilding earlier carries out VARPRO water fat decouples computation, will carry out image through the image after water fat separates then and merge, and obtains final image at last.
3. the water fat separation method based on the k-spatial data of owing to sample according to claim 1; It is characterized in that: in the step 5; Image after will rebuilding earlier carries out image and merges, and then the image after will merging carries out VARPRO water fat decouples computation, obtains final image at last.
4. the water fat separation method based on the k-spatial data of owing to sample according to claim 1 is characterized in that in the step 4, the method for said regularization iterative image reconstruction may further comprise the steps:
1) estimates initial pictures;
2) estimate present image;
3) confirm the direction of search;
4) carry out line search to upgrade step-length according to system matrix, MR raw data and the direction of search;
5) update image;
6) upgrade the direction of search;
7) judge whether to satisfy inner iteration and stop criterion, then do not return step 4) if do not satisfy; Then continue execution in step 8 if satisfy);
8) image after estimation improves;
9) judge whether to reach the greatest iteration step number of setting, if reach then execution in step 10); Otherwise judge whether to satisfy outside iteration and stop criterion, if satisfy then execution in step 10), otherwise return step 2);
10) output final image.
5. the water fat separation method based on the k-spatial data of owing to sample according to claim 1 is characterized in that in the step 5, said VARPRO water fat decouples computation may further comprise the steps:
The 1st step, initial field pattern are estimated, are set to matrix
Figure FDA0000060671680000021
The 2nd the step, to one group of inhomogeneous value
Figure FDA0000060671680000022
to all pixel precomputation cost functions
Figure FDA0000060671680000023
wherein
Figure FDA0000060671680000024
be the field unevenness lower limit;
Figure FDA0000060671680000025
is the upper limit of a unevenness, and scope
Figure FDA0000060671680000026
is split into L point;
Figure FDA0000060671680000027
representes l point; It is l ∈ [1, L];
The 3rd the step, for each the pixel q in the image by formula
Figure FDA0000060671680000028
The estimation of renewal field pattern, wherein δ qJ * the J that is pixel q faces the territory, and μ is the weight of the smoothing factor total amount of control Markov random field introducing,
Figure FDA0000060671680000029
Be the field unevenness of pixel q,
Figure FDA00000606716800000210
The field unevenness currency of remarked pixel j,
Figure FDA00000606716800000211
The new field unevenness estimated value of remarked pixel q, W Q, jThe weight factor of difference between expression control pixel q and the j;
The 4th step, the 3rd step of repetition change less than threshold xi until total field pattern; ξ＞0; Promptly
Figure FDA00000606716800000212
wherein; Q representes the total pixel number of field pattern,
Figure FDA00000606716800000213
the field unevenness currency of remarked pixel q;
The 5th step, basis
Figure FDA00000606716800000214
Calculate phase place
Figure FDA00000606716800000215
, S -τAnd S + τFor at the TE/2-τ of normal TE/2 echo both sides and the signal at TE/2+ τ place;
The 6th the step, for each pixel in the image, by formula
Figure FDA00000606716800000216
In conjunction with With
Figure FDA00000606716800000218
Calculate ρ wAnd ρ fWherein
Figure FDA00000606716800000219
Figure FDA00000606716800000220
ψ +Be the pseudo inverse matrix of ψ, I is N * N unit matrix,
Figure FDA00000606716800000221
The final output of expression field pattern,
Figure FDA00000606716800000222
Expression field pattern function,
Figure FDA00000606716800000223
Expression water and fatty density picture, For with f B0Signal cost function for variable; t 1, t 2... T MThe expression signal echo time; The set of signals that the different echo times of expression obtain, ρ wBe expressed as the signal intensity of water constituent, ρ fThe signal intensity of expression fat constituent.
6. the water fat separation method based on the k-spatial data of owing to sample according to claim 1 is characterized in that: in the step 1, said MR raw data is on the MR scanner, to fill track by sequence of setting and k-space to obtain.
7. the water fat separation method based on the k-spatial data of owing to sample according to claim 1 is characterized in that: in the step 2, said system matrix is non-homogeneous FFT system matrix and the inverse operation matrix that generates according to k-space tracking parameter.
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CN111133327A (en) * 2017-08-24 2020-05-08 皇家飞利浦有限公司 Dixon-type water/fat separation MR imaging
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CN110786854A (en) * 2019-11-05 2020-02-14 广州互云医院管理有限公司 Inversion recovery sequence T1 measurement method under water-fat mixed system
CN111047597A (en) * 2019-12-30 2020-04-21 中国科学院武汉物理与数学研究所 Multi-echo water-fat separation method based on deep learning
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