CN103513202B - DIXON water fat separation method in a kind of nuclear magnetic resonance - Google Patents

Abstract

The invention discloses the DIXON water fat separation method in a kind of nuclear magnetic resonance, comprise the steps: a) in magnetic resonance scan sequences, gather first to the 3rd totally three different echo-signal S1, S2 and S3, wherein the water fat signal precession phase contrast of first echo signal S1 and the 3rd echo-signal S3 is 2n π, n is natural number; B) the k-space signal of collection is changed into picture signal by Fourier transform; C) extract effective picture signal pixel at image area, and get the phase diagram of described effective picture signal pixel composite signal; Phase unwrapping is carried out to described phase diagram, obtains distribution of static magnetic field figure Δ B ₀; D) distribution of static magnetic field figure Δ B is utilized ₀, water images in described echo-signal is separated with fat image.DIXON water fat separation method provided by the invention, the echo time can require setting flexibly according to MR imaging sequences and application, can apply traditional DIXON algorithm process data, reduce the restriction arranged imaging sequence parameter simultaneously.

Description

DIXON water fat separation method in a kind of nuclear magnetic resonance

Technical field

The present invention relates to the water fat separation method in a kind of nuclear magnetic resonance, particularly relate to a kind of DIXON water fat separation method of improvement.

Background technology

Human body MRI(nuclear magnetic resonance) signal is mainly derived from two kinds of compositions: water and fat.The chemical bond of the Hydrogen Proton in hydrone is O-H key, and in fat molecule, the chemical bond of Hydrogen Proton is c h bond.Due to the difference of Hydrogen Proton ambient electron cloud distribution in these two kinds of structures, the magnetic field intensity causing Hydrogen Proton in hydrone to experience is slightly higher, finally cause the precession frequency of Hydrogen Proton in hydrone than Hydrogen Proton in fat molecule slightly hurry up, its difference is 3.5ppm, be equivalent to 150Hz/T, this precession frequency difference strengthens along with the increase of field intensity.Such as field intensity is 1.5T, hydrone 225Hz faster than the Hydrogen Proton precession frequency in fat molecule.

In the GRET1WI sequence that nuclear magnetic resonance is conventional, can by selecting the different echo times (TE) to obtain water and the positive and negative phase image of fat signal.

First same phase TE=1000ms ÷ ［ 150Hz/T × field intensity ］

First antiphase TE=, first same phase TE ÷ 2

Be 1.5T for field intensity, first same phase TE=1000 ÷ (150 × 1.5)=4.4ms

First antiphase TE=2.2ms

Utilize same phase and antiphase image, the image of independent " water " or " fat " signal can be produced:

W: the signal intensity of water; F: the signal intensity of fat

I is same: water and fatty same-phase signal; I is anti-: water and fatty antiphase signal

So:

I is with=W+F; I is anti-=W-F

Like this, two formulas are added respectively and subtract each other, and draw:

W=(I is anti-with+I)/2; F=(I is anti-with-I)/2

Just can carry out independent water or the imaging of fat, also be separate imaging of water and fat, be i.e. original DIXON technology [DixonWT, Simpleprotonspectroscopicimaging, Radiology153:189-194 (1984)].DIXON technology also can with doing SE or FSE sequence.

But when main field is uneven, original DIXON technology cannot realize water fat and be separated. only have the DIXON method after improving that adopts, by the many echo magnetic resonance signals of analyzing and processing, the water fat realized in the uneven situation of main field is separated.Relevant document has: GloverGH; SchneiderE; Three-pointDixontechniquefortruewater/fatdecompositionwi thBoinhomogeneitycorrection, MagneticResonanceinMedicine18:371-383 (1991); ZhangW, GoldhaberDM, KramerDM, SeparationofWaterandFatMRImagesinaSingleScanat35TUsing " Sandwich " Echoes, JournalofMagneticResonanceImaging6:909-917 (1996).

Traditional DIXON method generally all requires that in all echo-signals, water fat signal phase becomes homophase or anti-phase relation, and the echo time (TE) that thus can adopt imaging pulse sequence and relevant parameter have strict restriction.Such as under 1.5T field conditions, the anti-phase phase place precession time of water fat can only adopt 2.2 milliseconds, 6.6 milliseconds, 11.0 milliseconds etc., and the echo time of homophase can only adopt 4.4 milliseconds, 8.8 milliseconds, 13.2 milliseconds etc.This requirement brings unnecessary restriction to user in the selection of imaging sequence parameter.For field echo, phase place precession time equals the echo time; But for spin-echo sequence, phase place precession time is the deviation of actual ghosts time and desirable spin echo time.

XiangQing-San and AnLi has invented a kind of method being called DPE, sees XiangQS, AnL, Water-FatImagingwithDirectPhaseEncoding, JournalofMagneticResonanceImaging7:1002-1015 (1997).DPE method no longer limits the absolute relation of water fat phase place in echo-signal, and only requires that the phase place precession difference of water fat signal between echo is fixed amount.Although this provides motility to the echo time of pulse train and relative parameters setting, the special handling different from traditional DIXON must be carried out to obtained data.

ReederSB etc. adopted in 2005 the iterative algorithm process echo-signal of called after IDEAL to realize water fat and are separated, see ReederSB, PinedaAR, WenZ, ShimakawaA, YuH, BrittainJH, GoldGE, BeaulieuCHandPelcNJ, Iterativedecompositionofwaterandfatwithechoasymmetryandl east-squaresestimation (IDEAL): applicationwithfastspin-echoimaging, MagneticResonanceinMedicine54:636-644 (2005).IDEAL was not restricted in principle to the echo time, thus provided the setting of echo time in sequential parameter the most flexibly.But because the binary system involved by the imaging of water fat is non-linear, the method for least square optimized algorithm that IDEAL adopts easily is made mistakes by the interference of Local Minimum, causes the failure that water fat is separated.Although there is many improving one's methods in recent years, in order to reduce make mistakes may, but can not solve completely because the lowest point, local institute causes the root problem that the separation of water fat is failed.Therefore be necessary to improve DIXON method, ripe traditional DIXON algorithm process data can be applied, reduce the restriction that imaging sequence parameter is arranged simultaneously, and then DIXON method can be applied more neatly.

Summary of the invention

Technical problem to be solved by this invention is to provide the DIXON water fat separation method in a kind of nuclear magnetic resonance, echo time can set flexibly according to sequence requirements, traditional DIXON algorithm process data can be applied, reduce the restriction that imaging sequence parameter is arranged simultaneously.

The present invention solves the problems of the technologies described above the technical scheme adopted to be to provide DIXON water fat separation method in a kind of nuclear magnetic resonance, comprise the steps: a) in magnetic resonance scan sequences, gather first to the 3rd totally three different echo-signal S1, S2 and S3, wherein the water fat signal precession phase contrast of first echo signal S1 and the 3rd echo-signal S3 is 2n π, n is natural number; B) the k-space signal of collection is changed into picture signal by Fourier transform; C) extract effective picture signal pixel at image area, and get the phase diagram of described effective picture signal pixel composite signal; Phase unwrapping is carried out to described phase diagram, obtains distribution of static magnetic field figure Δ B ₀; D) distribution of static magnetic field figure Δ B is utilized ₀, water images in described echo-signal is separated with fat image.

Further, described step a) in three different echo-signal S1, S2 and S3 by representing as shown in the formula [1]:

$S_1=(W+{\mathrm{Fe}}^{i2\mathrm{\π\ΔfT}1})e^{\mathrm{i\γ\Δ}{B}_{0}T1}$

$S_2=(W+{\mathrm{Fe}}^{i2\mathrm{\π\ΔfT}2})e^{\mathrm{i\γ\Δ}{B}_{0}T2}$

$S_3=(W+{\mathrm{Fe}}^{i2\mathrm{\π\ΔfT}3})e^{\mathrm{i\γ\Δ}{B}_{0}T3}---\left[1\right]$

Wherein W and F is respectively the amplitude of water signal and fat signal, and Δ f is the difference of fat and water proton resonant frequency, and T1, T2 and T3 are respectively the phase place precession time of described echo-signal S1, S2 and S3.

Further, described step c) in extraction effective picture signal, be the amplitude of picture signal and the threshold value preset are compared, what be greater than described threshold value is effective picture signal.

Further, described step c) in distribution of static magnetic field figure Δ B ₀by calculating as shown in the formula [2]:

$S_3\×S_1^{*}=A^2{e}^{\mathrm{i\γ\Δ}{B}_0(T3-T1)}---\left[2\right]$

Wherein, A=|W+Fe ^{i2 π Δ fT1}| ≡ | W+Fe ^{i2 π Δ fT3}|

Then, distribution of static magnetic field figure $\mathrm{\Δ}{B}_0=\mathrm{unwrap}\left\{\arg \right[S_3\×S_1^{*}\left]\right\}/(T3-T1)/\mathrm{\γ}$

In formula for s ₁complex conjugate, arg [] asks phase angle for plural number, and unwrap{} represents phase unwrapping.

Further, described steps d) the amplitude W of water images and the amplitude F of fat image solved by following linear equation [3] and obtains:

W+a ₁F＝b ₁

W+a ₂F＝b ₂

W+a ₃F＝b ₃

W+a ₄F＝b ₄[3]

In formula:

a ₁＝cos(2πΔfT1)≡cos(2πΔfT3)

a ₂＝sin(2πΔfT1)≡sin(2πΔfT3)

a ₃＝cos(2πΔfT2)

a ₄＝sin(2πΔfT2)

$b_1=\mathrm{real}\{S_1\×e^{-\mathrm{i\γ\Δ}{B}_{0}T1}+S_3\×e^{-\mathrm{i\γ\Δ}{B}_{0}T3}\}/2$

$b_2=\mathrm{imag}\{S_1\×e^{-\mathrm{i\γ\Δ}{B}_{0}T1}+S_3\×e^{-\mathrm{i\γ\Δ}{B}_{0}T3}\}/2$

$b_3=\mathrm{real}\{S_2\×e^{-\mathrm{i\γ\Δ}{B}_{0}T2}\}$

$b_4=\mathrm{imag}{S}_2\×e^{-\mathrm{i\γ\Δ}{B}_{0}T2}\}$

Wherein cos () and sin () represents cosine and SIN function respectively; Real () and imag () represents respectively and asks input real and imaginary part.

Further, described step a) in three different echo-signal S1, S2 and S3 be field echo-signal [α, β, α+2n π], wherein 2 π Δ fT1=α, 2 π Δ fT2=β, 2 π Δ fT3=α+2n π.

Further, described step a) in echo-signal be flat field echo-signal, three different echo-signal S1, S2 and S3 are by once exciting rear change effective echo time to obtain.

Further, described step a) in three different echo-signal S1, S2 and S3 be spin echo signal [α, β, α+2n π], wherein 2 π Δ fT1=α, 2 π Δ fT2=β, 2 π Δ fT3=α+2n π, T1, T2 and T3 are respectively the deviation of point of each echo time and desirable spin echo position.

Further, described three different spin echo signal S1, S2 and S3 once excite acquisition after changing echo position by adjustment gradient fields balance.

The present invention contrasts prior art following beneficial effect: the DIXON water fat separation method in nuclear magnetic resonance provided by the invention, can at T1 sweep time, three different echo-signal S1 are gathered during T2 and T3=T1+2n π, S2 and S3, as long as the water fat signal precession phase contrast of first echo signal S1 and the 3rd echo-signal S3 is the even-multiple of π, to the time of whole echo group and intermediate echo, there is no the strict restriction of the interval in traditional DIXON algorithm, not only remain the advantage of traditional DIXON algorithm, and improve the motility of acquisition time, decrease the restriction that imaging sequence parameter is arranged.

Accompanying drawing explanation

Fig. 1 is magnetic resonance DIXON water fat separation process figure of the present invention;

Fig. 2 is magnetic resonance three field echo imaging sequence schematic diagrams in the embodiment of the present invention;

Fig. 3 adopts three field echoes to realize water fat separating effect figure in the embodiment of the present invention, wherein, Fig. 3 a be water fat add and together with image, Fig. 3 b is water images after being separated, and Fig. 3 c is for being separated rear fat image;

Fig. 4 is the free echo imaging sequence schematic diagram of magnetic resonance three in another embodiment of the present invention;

Fig. 5 adopts three spin echoes to realize water fat separating effect figure in the embodiment of the present invention, wherein, Fig. 5 a be water fat add and together with image, Fig. 5 b is water images after being separated, and Fig. 5 c is for being separated rear fat image.

Detailed description of the invention

Below in conjunction with drawings and Examples, the invention will be further described.

Fig. 1 is magnetic resonance DIXON water fat separation process schematic diagram of the present invention;

Please refer to Fig. 1, the magnetic resonance DIXON water fat separation method that imaging parameters provided by the invention is adjustable, comprises the steps:

Step S101, in magnetic resonance scan sequences, gather first to the 3rd totally three different echo-signal S1, S2 and S3, wherein the water fat signal precession phase contrast of first echo signal S1 and the 3rd echo-signal S3 is 2n π, n is natural number; Echo-signal S1, S2 and S3 are by representing as shown in the formula [1]:

$S_1=(W+{\mathrm{Fe}}^{i2\mathrm{\π\ΔfT}1})e^{\mathrm{i\γ\Δ}{B}_{0}T1}$

$S_2=(W+{\mathrm{Fe}}^{i2\mathrm{\π\ΔfT}2})e^{\mathrm{i\γ\Δ}{B}_{0}T2}$

$S_3=(W+{\mathrm{Fe}}^{i2\mathrm{\π\ΔfT}3})e^{\mathrm{i\γ\Δ}{B}_{0}T3}---\left[1\right]$

Wherein W and F is respectively water and fat signal amplitude, and Δ f is the difference of fat and water proton resonant frequency, Δ B ₀for distribution of static magnetic field figure, T1, T2 and T3 are respectively phase place precession time in echo-signal.For field echo, T1, T2 and T3 are consistent with the corresponding echo time; And for spin echo, what T1, T2 and T3 were corresponding is put the deviation with desirable spin echo position each echo time.

Step S102, changes into image by the k-space signal of collection by Fourier transform;

Step S103, extracts effective picture signal pixel at image area, and gets the phase diagram of described effective picture signal pixel composite signal; Phase unwrapping is carried out to described phase diagram, obtains distribution of static magnetic field figure Δ B ₀; Extract effective picture signal, be the amplitude of picture signal and the threshold value preset are compared, what be greater than described threshold value is effective picture signal.

Distribution of static magnetic field figure Δ B ₀by calculating as shown in the formula [2]:

$S_3\×S_1^{*}=A^2{e}^{\mathrm{i\γ\Δ}{B}_0(T3-T1)}---\left[2\right]$

Wherein, A=|W+Fe ^{i2 π Δ fT1}| ≡ | W+Fe ^{i2 π Δ fT3}|

Then, distribution of static magnetic field figure $\mathrm{\Δ}{B}_0=\mathrm{unwrap}\left\{\arg \right[S_3\×S_1^{*}\left]\right\}/(T3-T1)/\mathrm{\γ}$ In formula for s ₁complex conjugate, arg [] asks phase angle for plural number, and unwrap{} represents phase unwrapping.The reference material that relative phase launches has: JenkinsonM, Fast, Automated, N-DimensionalPhase-UnwrappingAlgorithm, MagneticResonanceinMedicine49:193 – 197 (2003); SzumowskiJ, CoshowWR, LiF, QuinnSFW, Phaseunwrappinginthethree-pointDixonmethodforfatsuppress ionMRimaging, Radiology192:555 – 561 (1994); SongSM-H, NapelS, PelcNJ, GloverGH, PhaseunwrappingofMRphaseimagesusingPoissonequation, IEEETransImageProcessing4:667 – 676 (1995).

Step S104, utilizes distribution of static magnetic field figure Δ B ₀, water images in described echo-signal is separated with fat image.。

The amplitude W of water images and the amplitude F of fat image is solved by following linear equation [3] and obtains:

W+a ₁F＝b ₁

W+a ₂F＝b ₂

W+a ₃F＝b ₃

W+a ₄F＝b ₄[3]

In formula:

a ₁＝cos(2πΔfT1)≡cos(2πΔfT3)

a ₂＝sin(2πΔfT1)≡sin(2πΔfT3)

a ₃＝cos(2πΔfT2)

a ₄＝sin(2πΔfT2)

$b_1=\mathrm{real}\{S_1\×e^{-\mathrm{i\γ\Δ}{B}_{0}T1}+S_3\×e^{-\mathrm{i\γ\Δ}{B}_{0}T3}\}/2$

$b_2=\mathrm{imag}\{S_1\×e^{-\mathrm{i\γ\Δ}{B}_{0}T1}+S_3\×e^{-\mathrm{i\γ\Δ}{B}_{0}T3}\}/2$

$b_3=\mathrm{real}\{S_2\×e^{-\mathrm{i\γ\Δ}{B}_{0}T2}\}$

$b_4=\mathrm{imag}{S}_2\×e^{-\mathrm{i\γ\Δ}{B}_{0}T2}\}$

Wherein cos () and sin () represents cosine and SIN function respectively; Real () and imag () represents respectively and asks input real and imaginary part.In formula [3] except W and F, other parameters are all known.Formula [3] linear equation is solved, W and F value can be obtained.Obtaining W and F value by solving system of linear equations shown in formula [3] to each as number, water images and fat image can be obtained respectively.

Embodiment 1

Fig. 2 is magnetic resonance three field echo imaging sequence schematic diagrams in the embodiment of the present invention.Fig. 3 adopts three field echoes to realize water fat separating effect figure in the embodiment of the present invention, wherein, Fig. 3 a is the image of water together with fat, and Fig. 3 b is water images after being separated, and Fig. 3 c is for being separated rear fat image.

Please refer to Fig. 1 and Fig. 2, the magnetic resonance DIXON water fat separation method that the embodiment of the present invention provides adopts three field echoes to realize water fat and is separated, and specifically comprises the steps:

Step S101: apply magnetic resonance field echo imaging sequence as shown in Figure 2, make 2 π Δ fT1=α by arranging, 2 π Δ fT2=β and 2 π Δ fT3=α+2n π, can collect three field echo datas that [α, β, α+2n π] combines.[α, β, α+2n π] combination refers in three echo-signals, and the phase relation of water signal and fat signal is respectively α, β and α+2n π, and wherein n is natural number.For 1.5T field intensity, (T1, T2, the T3) that meet above condition selects can be (τ 1, τ 2, τ 1+4.4) or (τ 1, τ 2, τ 1+8.8) millisecond etc.For 3T field intensity, (T1, T2, T3) selects can be (τ 1, τ 2, τ 1+2.2) or (τ 1, τ 2, τ 1+4.5) millisecond etc., and wherein τ 1, τ 2 can set flexibly according to sequence requirements;

Step S102: gathered k-space signal is changed into image by Fourier transformation;

Step S103: extract effective picture signal pixel at image area, and get the phase diagram of described effective picture signal pixel composite signal; Phase unwrapping is carried out to described phase diagram, obtains distribution of static magnetic field figure Δ B ₀; Extract effective picture signal, be the amplitude of each image pixel signal and the threshold value preset are compared, what be greater than described threshold value is effective picture signal.Distribution of static magnetic field figure Δ B ₀calculate according to above-mentioned formula [2].

Step S104: utilize distribution of static magnetic field figure Δ B ₀, water images in described echo-signal is separated with fat image.Phase diagram according to launching calculates each parameter of above-mentioned formula [3] system of linear equations; Linear solution formula [3] obtains water and fat signal amplitude; Finally obtain water and fat image, as shown in Fig. 3 b and Fig. 3 c.

Embodiment 2

Fig. 4 is magnetic resonance three spin echo imaging sequence schematic diagrams in another embodiment of the present invention; Fig. 5 adopts three spin echoes to realize water fat separating effect figure in the embodiment of the present invention, wherein, Fig. 5 a is the image of water together with fat, and Fig. 5 b is the water images after being separated, and Fig. 5 c is the fat image after being separated.

Please refer to Fig. 1 and Fig. 4, the magnetic resonance DIXON water fat separation method that the embodiment of the present invention provides adopts three spin echoes to realize water fat and is separated, and specifically comprises the steps:

Step S101: select MR imaging sequences shown in Fig. 4, make 2 π Δ fT1=α by arranging, 2 π Δ fT2=β and 2 π Δ fT3=α+2n π, can obtain three spin echo data that [α, β, α+2n π] combines.[α, β, α+2n π] combination refers in three echo-signals, and the phase relation of water signal and fat signal is respectively α, β and α+2n π.For 1.5T field intensity, (T1, T2, the T3) that meet above condition selects can be (τ 1, τ 2, τ 1+4.4) or (τ 1, τ 2, τ 1+8.8) millisecond etc.For 3T field intensity, (T1, T2, T3) selects can be (τ 1, τ 2, τ 1+2.2) or (τ 1, τ 2, τ 1+4.4) millisecond etc., and wherein τ 1, τ 2 can set flexibly according to sequence requirements.

Step S102: gathered k-space signal is changed into image by Fourier transformation.

Step S103: extract effective picture signal pixel at image area, and get the phase diagram of described effective picture signal pixel composite signal; Phase unwrapping is carried out to described phase diagram, obtains distribution of static magnetic field figure Δ B ₀; Extract effective picture signal, be the amplitude of each image pixel signal and the threshold value preset are compared, what be greater than described threshold value is effective picture signal., distribution of static magnetic field figure Δ B ₀calculate according to above-mentioned formula [2].

Step S104: utilize distribution of static magnetic field figure Δ B ₀, water images in described echo-signal is separated with fat image.Phase diagram according to launching calculates each parameter of above-mentioned formula [3] system of linear equations; Linear solution formula [3] obtains water and fat signal amplitude; Finally obtain water and fat image, as shown in Fig. 5 b and Fig. 5 c.

The echo-signal that the present invention adopts is not limited to simple field echo and spin echo, also other imaging sequences and method can be adopted to obtain, such as echo planar imaging (EPI), spiralscan, the formation methods such as fastspin-echo (FSE), parallelimaging (PI) all can adopt the inventive method to realize water fat and be separated.Three echo-signals used, can adopt and once excite rear many echo acquirements to obtain as above, also can repeatedly excite to gather to obtain.

For flat field echo (field-echoEPI), the present invention's three echo-signals used can obtain by changing effective echo time (apparentTE).Adopt the step S101 to S105 in above two embodiments to realize water fat to signal processing to be separated.SE class sequence uses 180 degree of focusing pulses to gather echo-signal, the phase contrast that there is water proton and fat proton before pulse is applied takes a turn for the worse by 180 degree of focusing pulses, echo after pulse applies produces moment (TE) this phase contrast and will disappear completely, therefore conventional SE or FSE sequence echo acquisition technique is adopted, no matter how TE selects, what obtain is all same phase image, can not obtain antiphase image.If adopt FSE sequence, three different echo-signals can change echo position by adjustment gradient fields EQUILIBRIUM CALCULATION FOR PROCESS and obtain, and adopt identical signal processing step to realize water fat afterwards and be separated.

To sum up, the magnetic resonance DIXON water fat separation method that imaging parameters provided by the invention is adjustable, can at T1 sweep time, three different echo-signal S1 are gathered during T2 and T3, S2 and S3, as long as the water fat signal precession phase contrast of first echo signal S1 and the 3rd echo-signal S3 is the even-multiple of π, to the time of whole echo group and intermediate echo, there is no the strict restriction of the interval in traditional DIXON algorithm, not only remain the advantage of traditional DIXON algorithm, and improve the motility of acquisition time, decrease the restriction that imaging sequence parameter is arranged.

Although the present invention discloses as above with preferred embodiment; so itself and be not used to limit the present invention, any those skilled in the art, without departing from the spirit and scope of the present invention; when doing a little amendment and perfect, therefore protection scope of the present invention is when being as the criterion of defining with claims.

Claims (8)

1. the DIXON water fat separation method in nuclear magnetic resonance, is characterized in that, comprise the steps:

A) in magnetic resonance scan sequences, gather first to the 3rd totally three different echo-signal S1, S2 and S3, wherein the water fat signal precession phase contrast of first echo signal S1 and the 3rd echo-signal S3 is 2n π, n is natural number, and first echo signal S1 and the echo time corresponding to second echo signal S2 can set flexibly according to sequence requirements;

B) the k-space signal of collection is converted to picture signal by Fourier transform;

C) extract effective picture signal pixel at image area, and get the phase diagram of described effective picture signal pixel composite signal; Phase unwrapping is carried out to described phase diagram, obtains distribution of static magnetic field figure Δ B ₀; Described extraction effective picture signal, be the amplitude of picture signal and the threshold value preset are compared, what be greater than described threshold value is effective picture signal;

D) distribution of static magnetic field figure Δ B is utilized ₀, water images in described echo-signal is separated with fat image.

2. DIXON water fat separation method as claimed in claim 1, is characterized in that, described step a) in three different echo-signal S1, S2 and S3 by representing as shown in the formula [1]:

$S1=(W+{\mathrm{Fe}}^{i2\mathrm{\π}\mathrm{\Δ}fT1})e^{{\mathrm{i\γ\ΔB}}_{0}T1}$

$S2=(W+{\mathrm{Fe}}^{i2\mathrm{\π}\mathrm{\Δ}fT2})e^{{\mathrm{i\γ\ΔB}}_{0}T2}$

$S3=(W+{\mathrm{Fe}}^{i2\mathrm{\π}\mathrm{\Δ}fT3})e^{{\mathrm{i\γ\ΔB}}_{0}T3}---\[1\]$

Wherein W and F is respectively the amplitude of water signal and fat signal, and Δ f is the difference of fat and water proton resonant frequency, and T1, T2 and T3 are respectively the phase place precession time of described echo-signal S1, S2 and S3, and γ is gyromagnetic ratio.

3. DIXON water fat separation method as claimed in claim 2, is characterized in that, described step c) in distribution of static magnetic field figure Δ B ₀by calculating as shown in the formula [2]:

$S3\×S{1}^{*}=A^2{e}^{{\mathrm{i\γ\ΔB}}_0(T3-T1)}---\[2\]$

Wherein, A=|W+Fe ^{i2 π Δ fT1}| ≡ | W+Fe ^{i2 π Δ fT3}|

Then, distribution of static magnetic field figure ${\mathrm{\ΔB}}_0=\frac{unwrap\left\{\arg (S3\×S{1}^{*})\right\}}{(T3-T1)\mathrm{\γ}}$

S1 in formula ^*for the complex conjugate of S1, arg [] asks phase angle for plural number, and unwrap{} represents phase unwrapping, the coefficient in A representation formula.

4. DIXON water fat separation method as claimed in claim 3, is characterized in that, described steps d) the amplitude W of water images and the amplitude F of fat image solved by following linear equation [3] and obtains:

W+a ₁F＝b ₁

W+a ₂F＝b ₂

W+a ₃F＝b ₃

W+a ₄F＝b ₄[3]

In formula:

a ₁＝cos(2πΔfT1)≡cos(2πΔfT3)

a ₂＝sin(2πΔfT1)≡sin(2πΔfT3)

a ₃＝cos(2πΔfT2)

a ₄＝sin(2πΔfT2)

$b_1=real\{S1\×e^{-{\mathrm{i\γ\ΔB}}_{0}T1}+S3\×e^{-{\mathrm{i\γ\ΔB}}_{0}T3}\}/2$

$b_2=imag\{S1\×e^{-{\mathrm{i\γ\ΔB}}_{0}T1}+S3\×e^{-{\mathrm{i\γ\ΔB}}_{0}T3}\}/2$

$b_3=real\{S2\×e^{-{\mathrm{i\γ\ΔB}}_{0}T2}\}$

$b_4=imag\{S2\×e^{-{\mathrm{i\γ\ΔB}}_{0}T2}\}$

Wherein cos () and sin () represents cosine and SIN function respectively, and real () and imag () represents respectively and asks input real and imaginary part, a ₁, a ₂, a ₃, a ₄, b ₁, b ₂, b ₃, b ₄coefficient all in representation formula.

5. the DIXON water fat separation method as described in claim arbitrary in claim 1-4, it is characterized in that, described step a) in three different echo-signal S1, S2 and S3 be field echo-signal, and the phase relation of water signal and fat signal is [α in described three echo-signals, β, α+2n π], wherein 2 π Δ fT1=α, 2 π Δ fT2=β, 2 π Δ fT3=α+2n π.

6. DIXON water fat separation method as claimed in claim 5, is characterized in that, described step a) in echo-signal be flat field echo-signal, three different echo-signal S1, S2 and S3 are by once exciting rear change effective echo time to obtain.

7. the DIXON water fat separation method as described in claim arbitrary in claim 1-4, it is characterized in that, described step a) in three different echo-signal S1, S2 and S3 be spin echo signal, and in three echo-signals, the phase relation of water signal and fat signal is wherein 2 π Δ fT1=α, 2 π Δ fT2=β, 2 π Δ fT3=α+2n π, T1, T2 and T3 are respectively the deviation of point of each echo time and desirable spin echo position.

8. DIXON water fat separation method as claimed in claim 7, is characterized in that, described three different spin echo signal S1, S2 and S3 once excite acquisition after changing echo position by adjustment gradient fields balance.