CN105232046A - Method for single sweep quantitative magnetic resonance T2 imaging based on overlapping echoes - Google Patents

Abstract

The invention provides a method for single sweep quantitative magnetic resonance T2 imaging based on overlapping echoes and relates to a magnetic resonance imaging method. Echo signals of two different evolution time are generated by adding two excitation pulses with the same deflection angle in single sweep. Though the evolution time of the two echo signals is different, the T2 weighing of the two echo signals is caused to be different, the two echo signals come from the same imaging slice, the two echo signals can be separated through prior knowledge between the two echo signals, namely the structural similarity in combination with edge sparsity, and the two echo signals are separated by utilizing a separation algorithm corresponding to sparse conversion matching; and finally the two signals obtained through separation undergo T2 calcualtion to obtain a quantitative T2 image. The quantitative T2 imaging in single sweep is acquired, the time of quantitative T2 imaging is reduced from the second grade and even minute grade to the ms grade, and the quality of the acquired T2 image can be equivalent to the quality of an image obtained in an EPI sequence in conventional single sweep.

Description

A kind of single sweep Quantitative MRI Measurement T2 formation method based on overlapping echo

Technical field

The present invention relates to the method for nuclear magnetic resonance, especially relate to a kind of single sweep Quantitative MRI Measurement T2 formation method based on overlapping echo.

Background technology

Magnetic resonance parameters imaging (T2 imaging, T2 ^*imaging and diffusion imaging) quantitative information of abundant tissue signature's attribute can be provided and ([1] B.Zhao that has a wide range of applications in clinical diagnosis because of it, F.Lam, andZ.P.Liang, " Model-basedMRParametermappingwithsparsityconstraints:par ameterestimationandperformancebounds; " IEEETrans.Med.Imag., vol.33, no.9, pp.1832-1844,2014), such as: whether the diagnosis of myocardial infarction, to measure iron content in liver excessive etc.Especially, the quantitative analysis in T2 relaxation time causes increasing concern in the clinical medicine nuclear magnetic resonances such as psychiatry and neuropathy section.But magnetic resonance parameters is imaged in its imaging process the image often needing to obtain a series of contrast weight, thus general its obtains the chronic of data.Although have now much different formation methods put forward overcome the problems referred to above, such as: down-sampling spin echo magnetic resonance imaging (Spin-EchoMRI), gradient spin echo nuclear magnetic resonance (GradientSpinEchoMRI), parallel imaging (ParallelImagingwithCS) etc. based on compressed sensing.Meanwhile, some method for reconstructing based on model and the method for reconstructing based on Bloch emulation are suggested in succession, accelerate the speed of imaging with this further.But the magnetic resonance parameters formation method repeatedly excited still needs to expend the time of several seconds in the acquisition stage, like this real-time parameter imaging is carried out to unrepeatable neural activity and just become task in the cards hardly.Therefore, Echo-plane imaging (the echo-planarimaging of many echoes of single sweep, EPI) formation method is suggested ([2] S.Posse, S.Wiese, D.Gembris, K.Mathiak, C.Kessler, M.L.Grosse-Ruyken, B.Elghawaghi, T.Richards, S.R.Dager, andV.G.Kiselev, " EnhancementofBOLD-ContrastSensitivitybySingle-ShotMulti-EchoFunctionalMRImaging, " Magn.Reson.Med., vol.42, pp.87 – 97, 1999), the method is by being included in the acquisition of a series of contrast weight image in multiple echoes of obtaining in single pass.But this method exists limitation, be that this method needs to extend echo train on the one hand, the decay increasing time and the signal obtained must be caused; Be on the other hand the realization of this method compared with conventional EPI method to extend the repetition time (TR) for cost, this just may need the spatial resolution of sacrifice gained echo; And the most important thing is that this method can only be used for T2* quantitative imaging at present, the method that there is no is for T2 quantitative imaging.In addition, although there is different quick T2 formation methods to be in succession suggested, comprise gradient spin echo sequence, these methods are all carry out T2 imaging by repeatedly excitation sequence, and so not only effect is barely satisfactory, and imaging efficiency is also in urgent need to be improved.

Summary of the invention

The object of the present invention is to provide a kind of single sweep Quantitative MRI Measurement T2 formation method based on overlapping echo.

The present invention includes following steps:

(1) on magnetic resonance imager operating board, open the function software in magnetic resonance imager, first area-of-interest location is carried out to imaging object, then carry out tuning, shimming, capability correction and frequency correction;

(2) OLED imaging sequence compiled is in advance imported; According to concrete experimental conditions, the parameters of pulse train is set;

The structure of described OLED imaging sequence is followed successively by: flip angle is that the sheet of α selects pulse, (TE ₂-TE ₁)/2, flip angle are that the sheet of α selects pulse, TE ₁/ 2,180 ° of reunion pulses, sampled echo chain;

By two low-angle excitation pulses in conjunction with two echo shift gradient G ₁and G ₂, make two echoes produce skew at the center in K space, described 180 ° of reunion pulses and two low-angle excitation pulses all select gradient G with layer _sscombine and carry out layer choosing; Echo time delay (TE is applied respectively before and after second low-angle excitation pulse ₂-TE ₁)/2 and TE ₁/ 2, there is x before and after described 180 ° of reunion pulses, the destruction gradient effect in y, z tri-directions;

Described sampled echo chain is by acting on x respectively, the gradient chain composition in y direction; The gradient chain in x direction is made up of a series of positive negative gradient, and the area of each gradient is first echo shift gradient G ₁three times; The gradient chain in y direction is made up of a series of equal-sized " blips " gradient, and the gross area of described " blips " gradient equals four times of displacement gradient area;

Before described sampled echo chain, x and y direction is applied with reunion gradient G respectively _rorand G _ar, described G _rorarea be the half of first the gradient area in x direction, direction is contrary with first, x direction gradient direction; Described G _ararea be the half of the gross area of all described " blips " gradients, direction is contrary with described " blips " gradient direction;

(3) perform the described OLED imaging sequence that step (2) sets, carry out data sampling; The K space data of two echo-signals is obtained after data sampling completes;

(4) K space data obtained step (3) is analyzed and to echo-signal magnetization vector M ₊evolution carry out theoretical derivation, second echo shift gradient G ₂afterwards, following formula can be obtained:

$M_{+}=\underset{\stackrel{\→}{r}}{\∫}\mathrm{\ρ}\left(\stackrel{\→}{r}\right)\sin \mathrm{\α}\{-i{\mathrm{cos\αe}}^{{\mathrm{i\θ}}_2}+\frac{1}{2}{e}^{-\mathrm{\δ}TE/T_2\left(\stackrel{\→}{r}\right)}\[(1+\cos \mathrm{\α})e^{i({\mathrm{\θ}}_2-{\mathrm{\θ}}_1)}+(1-\cos \mathrm{\α})e^{i({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)}\]\}d\stackrel{\→}{r}$

In formula be spin density distribution, α is the flip angle of excitation pulse, found through experiments, and when α=45 °, the intensity of two echo-signals is all relatively high, δ TE=(TE ₂-TE ₁)/2, wherein δ ₁, δ ₂the persistent period of first and second corresponding respectively echo shift gradient, γ is gyromagnetic ratio; From above formula, in fact have three echo-signals of being modulated by out of phase, wherein Section 1 is produced by second excitation pulse, and then two are produced by first excitation pulse; But will to isolate these three signals relative to the signal that single sweep obtains be very complicated, by analyzing latter two, the echo center of known latter two is different, and last signal intensity is relative to smaller Section 2, therefore last echo can be left in the basket by simple process;

(5) echo-signal that step (4) obtains is separated with following separation algorithm, theoretical according to Fourier transformation, two echo-signals are different in the linear phase of image area, in addition, although two echo-signals cause T2 weighting different due to evolution time difference, they are from same image layer; Therefore, the prior information that the picture structure of both utilizations is similar can combine reconstruction to two echo-signals, and algorithm for reconstructing is as follows:

$\{x_1,x_2\}=\underset{x_1,x_2}{\arg \min }\[\left|\right|x_1-x_{10}|{|}_2^2+{\mathrm{\λ}}_1||\▿x_1|{|}_1+{\mathrm{\λ}}_2\left|\right|\▿x_2|{|}_1+{\mathrm{\λ}}_3||\▿(x_1-{\mathrm{\βx}}_2)|{|}_1\]$

Wherein, x ₁, x ₂the image rebuilding out from first and second echo-signal respectively; scale factor, x ₁₀, x ₂₀the initial pictures of first and second echo-signal respectively; λ ₁, λ ₂and λ ₃lagrange's method of multipliers adjustable constraint weight respectively; ▽ is gradient operator; Section 1 is fidelity item, and Section 2 and Section 3 are the sparsity constraints to the first width and the second width image, and last is two width image outline similarity constraint; This two width image has following relation:

Wherein, the linear phase displacement of the first width and the second width image respectively; x ₀being primary signal, is carry out inverse Fourier transform by the primary signal comprising first and second echo-signal to obtain, and solves by iterative algorithm the image that above-mentioned formula just can obtain first after being separated and second echo-signal generation;

(6) image that step (5) is separated carries out T2 imaging calculating; For the T2 formation method of single sweep, the echo time image only needing two width different is just feasible, and the value of T2 is directly tried to achieve by T2 relaxation equation:

$T_2\left(r\right)=\frac{-\mathrm{\Δ}TE}{ln\left(\mathrm{\μ}\frac{S_2\left(\stackrel{\→}{r}\right)}{S_1\left(\stackrel{\→}{r}\right)}\right)},$

Wherein correction factor, Δ TE=TE ₂-TE ₁; S ₁and S ₂the image intensity of first echo-signal and second echo-signal respectively, add full variation (TotalVariation) extrapolation to strengthen the resolution of image, and a setting threshold value, when the numerical value obtained is lower than threshold value, can noise be considered to and be left in the basket, same is also irrational when the T2 value calculated is excessive, also can be omitted; The T2 image of the high-quality with better resolution has been calculated finally by T2 imaging.

The invention provides a kind of when single pass, obtain overlapping echo-signal, then utilize the signal of separation algorithm to overlap to be separated, finally carry out T2 calculating, just can obtain a kind of new formation method suitable with resolution with the acquisition time required for conventional single sweep EPI sequence.

The present invention by adding the echo-signal that two have the excitation pulse at equal deflection angle to produce two different evolution times in single sweep operation, although the evolution time of two echo-signals is different, cause the T2 weighting of two echo-signals different, but these two echo-signals are from same imaging slice, therefore the priori between two echo-signals can be passed through: both similar, associating the openness of edge are separated this two echo-signals, thus utilize sparse transformation to coordinate corresponding separation algorithm to be separated these two echo-signals.Two signals finally obtained separation carry out T2 and calculate quantitative T2 image.Utilize the method first to obtain the quantitative T2 imaging of single sweep operation, by the time of quantitative T2 imaging by level second even minute level, reduce to ms level, and the picture quality that the T2 picture quality obtained can obtain with the single sweep operation EPI sequence of routine is suitable.

Accompanying drawing explanation

Fig. 1 is OLED imaging sequence structure chart in the present invention.

Fig. 2 illustrates the Comparative result figure of the model experiment of OLED imaging sequence.Wherein:

(a) be separated before the image comprising two echo-signals that goes out of OLED rebuilding series;

(b) be from (a) be separated after first echo-signal image;

(c) be from (a) be separated after second echo-signal image;

D () is the signal pattern that many scannings single echo spin-echo sequence (SE sequence) reconstruct;

E () is the signal pattern that single sweep spin EPI rebuilding series goes out;

G () is the T2 image rebuild from (a) out;

H () is respectively along signal strength values and the T2 value of respective dashed part of horizontal section in (d) and (e).

Fig. 3 is the T2 image rebuild from Fig. 2 (d) out.

Detailed description of the invention

Below in conjunction with the drawings and the specific embodiments, the present invention will be further described.

Each step in specific implementation process of the present invention is as follows:

(1) on magnetic resonance imager operating board, open corresponding function software in imager, first area-of-interest location is carried out to imaging object, then carry out tuning, shimming, power and frequency correction;

(2) OLED imaging sequence compiled is in advance imported; According to concrete experimental conditions, the parameters of pulse train is set;

The structure of described OLED imaging sequence is followed successively by: flip angle is that the sheet of α selects pulse, (TE ₂-TE ₁)/2, flip angle are that the sheet of α selects pulse, TE ₁/ 2,180 ° of reunion pulses, sampled echo chain;

By two low-angle excitation pulses in conjunction with two echo shift gradient G ₁and G ₂, thus making two echoes produce skew at the center in K space, described 180 ° of reunion pulses and two low-angle excitation pulses all select gradient G with layer _sscombine and carry out layer choosing; Echo time delay (TE is applied respectively before and after second low-angle excitation pulse ₂-TE ₁)/2 and TE ₁/ 2, there is x before and after described 180 ° of reunion pulses, the destruction gradient effect in y, z tri-directions;

Described sampled echo chain is by acting on x respectively, the gradient chain composition in y direction; The gradient chain in x direction is made up of a series of positive negative gradient, and the area of each gradient is described displacement gradient G ₁three times; The gradient chain in y direction is made up of a series of equal-sized " blips " gradient, and the gross area of described " blips " gradient equals four times of described displacement gradient area;

Before described sampled echo chain, x and y direction is applied with reunion gradient G respectively _rorand G _ar, described G _rorarea be the half of first the gradient area in x direction, direction is contrary with first, x direction gradient direction; Described G _ararea be the half of the gross area of all described " blips " gradients, direction is contrary with described " blips " gradient direction;

(3) perform the described OLED imaging sequence that step (2) sets, carry out data sampling; The K space data of two echo-signals is obtained after data sampling completes.

(4) K space data obtained step (3) is analyzed and to echo-signal magnetization vector M ₊evolution carry out theoretical derivation, second displacement gradient G ₂afterwards, following formula can be obtained:

$M_{+}=\underset{\stackrel{\→}{r}}{\∫}\mathrm{\ρ}\left(\stackrel{\→}{r}\right)\sin \mathrm{\α}\{-i{\mathrm{cos\αe}}^{{\mathrm{j\θ}}_2}+\frac{1}{2}{e}^{-\mathrm{\δ}TE/T_2\left(\stackrel{\→}{r}\right)}\[(1+\cos \mathrm{\α})e^{i({\mathrm{\θ}}_2-{\mathrm{\θ}}_1)}+(1-\cos \mathrm{\α})e^{i({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)}\]\}d\stackrel{\→}{r}$

In formula be spin density distribution, α is the flip angle of excitation pulse, found through experiments, and when α=45 °, the intensity of two echo-signals is all relatively high, δ TE=(TE ₂-TE ₁)/2, wherein δ ₁, δ ₂the persistent period of first and second corresponding respectively echo shift gradient, γ is gyromagnetic ratio.In fact have three echo-signals of being modulated by out of phase by above formula is known, wherein Section 1 is produced by second excitation pulse, and then two are produced by first excitation pulse; But will to isolate these three signals relative to the signal that single sweep obtains be very complicated, by analyzing latter two, the echo center of known latter two is different, and last signal intensity is relative to smaller Section 2, therefore last echo can be left in the basket by simple process.

(5) echo-signal that step (4) obtains is separated with following separation algorithm, theoretical according to Fourier transformation, two echo-signals are different in the linear phase of image area, in addition, although two echo-signals cause T2 weighting different due to evolution time difference, they are from same image layer.Therefore, the prior information that the picture structure of both utilizations is similar can combine reconstruction to two echo-signals.Algorithm for reconstructing is as follows:

$\{x_1,x_2\}=\underset{x_1,x_2}{\arg \min }\[\left|\right|x_1-x_{10}|{|}_2^2+k||\▿x_1|{|}_1+{\mathrm{\λ}}_2\left|\right|\▿x_2|{|}_1+L||\▿(x_1-{\mathrm{\βx}}_2)|{|}_1\]$

Wherein x ₁, x ₂the image rebuilding out from first and second echo-signal respectively; scale factor, x ₁₀, x ₂₀the initial pictures of first and second echo-signal respectively; λ ₁, λ ₂and λ ₃lagrange's method of multipliers adjustable constraint weight respectively; ▽ is gradient operator.Section 1 is fidelity item, and Section 2 and Section 3 are the sparsity constraints to the first width and the second width image, and last is two width image outline similarity constraint.This two width image has following relation:

Wherein the linear phase displacement of the first width and the second width image respectively; x ₀being primary signal, is carry out inverse Fourier transform by the primary signal comprising first and second echo-signal to obtain.The image that above-mentioned formula just can obtain first after being separated and second echo-signal generation is solved by iterative algorithm.

(6) image that step (5) is separated carries out T2 imaging calculating.For the T2 formation method of single sweep, the echo time image only needing two width different is just feasible, and the value of T2 is directly tried to achieve by T2 relaxation equation:

$T_2\left(r\right)=\frac{-\mathrm{\Δ}TE}{ln\left(\mathrm{\μ}\frac{S_2\left(\stackrel{\→}{r}\right)}{S_1\left(\stackrel{\→}{r}\right)}\right)},$

Wherein correction factor, Δ TE=TE ₂-TE ₁; S ₁and S ₂the image intensity of first echo-signal and second echo-signal respectively.Here we add full variation (TotalVariation) extrapolation to strengthen the resolution of image, and we set a threshold value, when the numerical value obtained is left in the basket lower than being considered to noise during threshold value, same is also irrational when the T2 value calculated is excessive, also can be omitted.The T2 image of the high-quality with better resolution has been calculated finally by T2 imaging.

Below provide specific embodiment:

Carry out water model experiment with the single sweep Quantitative MRI Measurement T2 formation method based on overlapping echo, be used for verifying feasibility of the present invention.Before experiment first by be contained in concentration in seven ampoule be 0.5% agar gel with containing the manganous chloride (MnCl2 of variable concentrations, 0.01 ~ 0.16mM) aqueous solution, be used for producing a series of T2 values close to tissue, and making the ratio of T1/T2 be about 10 in 3T imager, the ratio of this and tissue T1 and T2 under 3T magnetic field is suitable.Test its time range of T1 value recorded and be approximately 350 ~ 1500ms.In addition, to scan T2 image that single echo spin-echo sequence (SE sequence) produces as a reference, its imaging thickness is 2mm more.First we import the compiled single sweep separating plane imaging sequence based on overlapping echo as shown in Figure 1, and arrange test parameters, the test parameters of the present embodiment arranges as follows: the firing time of 45 ° of excitation pulses is 3ms, x direction sampling number N _xbe 128, y direction sampling number N _ybe 64, sampling bandwidth sw is 91.4kHz.The visual field FOV in x direction _xfor the visual field FOV in 20cm, y direction _yfor 20cm.After above test parameters being set, the sampling time directly running whole sequence is about 160ms.After sampling terminates, just obtain the sampled data of overlapping echo-signal.Then we just utilize the separation algorithm in step (5) to be separated two of overlap echo-signals, separation algorithm here we regularization parameter is set to λ respectively ₁=1.4, λ ₂=1, λ ₃=1.As shown in Figures 2 and 3, SE sequence adopts 8 different echo time delays (from 8.8 ~ 120ms not etc.) to result after separation, and its sampling matrix size is 128 × 128, TR=3.5s, and total sweep time is approximately 1h.Can see there is obvious distortion from figure a and figure e, this causes because ambient field is uneven.It should be noted that figure d and arrow indicating section in figure e, the signal intensity originally in each water pipe should be uniform, and in figure, the signal intensity of indicating section is uneven.This may be caused by many factors comprehensive function, the susceptiveness difference of wherein uneven ambient field and magnetic test coil is the main cause causing spin-echo sequence image uneven, and the pile up effect of signal is also the main cause that this phenomenon appears in single sweep EPI sequence in non-uniform field.Can find from Fig. 2 h, although the signal intensity of EPI is more uneven, its T2 value but than signal intensity evenly.Therefore test the sequence pair non-uniform field that adopts and coil sensitivity diversity ratio spin echo EPI sequence robustness stronger.Can prove thus, OLED formation method, when once exciting, overlapping echo-signal can be obtained, utilize corresponding separation algorithm to be separated, decrease acquisition time, improve the spatial resolution of image.

Table 1

Each symbol description is see table 1.

Claims (1)

1., based on a single sweep Quantitative MRI Measurement T2 formation method for overlapping echo, it is characterized in that comprising the steps:

(1) on magnetic resonance imager operating board, open the function software in magnetic resonance imager, first area-of-interest location is carried out to imaging object, then carry out tuning, shimming, capability correction and frequency correction;

(2) OLED imaging sequence compiled is in advance imported; According to concrete experimental conditions, the parameters of pulse train is set;

The structure of described OLED imaging sequence is followed successively by: flip angle is that the sheet of α selects pulse, (TE ₂-TE ₁)/2, flip angle are that the sheet of α selects pulse, TE ₁/ 2,180 ° of reunion pulses, sampled echo chain;

By two low-angle excitation pulses in conjunction with two echo shift gradient G ₁and G ₂, make two echoes produce skew at the center in K space, described 180 ° of reunion pulses and two low-angle excitation pulses all select gradient G with layer _sscombine and carry out layer choosing; Echo time delay (TE is applied respectively before and after second low-angle excitation pulse ₂-TE ₁)/2 and TE ₁/ 2, there is x before and after described 180 ° of reunion pulses, the destruction gradient effect in y, z tri-directions;

Described sampled echo chain is by acting on x respectively, the gradient chain composition in y direction; The gradient chain in x direction is made up of a series of positive negative gradient, and the area of each gradient is first echo shift gradient G ₁three times; The gradient chain in y direction is made up of a series of equal-sized " blips " gradient, and the gross area of described " blips " gradient equals four times of displacement gradient area;

Before described sampled echo chain, x and y direction is applied with reunion gradient G respectively _rorand G _ar, described G _rorarea be the half of first the gradient area in x direction, direction is contrary with first, x direction gradient direction; Described G _ararea be the half of the gross area of all described " blips " gradients, direction is contrary with described " blips " gradient direction;

(3) perform the described OLED imaging sequence that step (2) sets, carry out data sampling; The K space data of two echo-signals is obtained after data sampling completes;

(4) K space data obtained step (3) is analyzed and to echo-signal magnetization vector M ₊evolution carry out theoretical derivation, second echo shift gradient G ₂afterwards, following formula can be obtained:

$M_{+}=\underset{\stackrel{\→}{r}}{\∫}\mathrm{\ρ}\left(\stackrel{\→}{r}\right)\sin \mathrm{\α}\{-i{\mathrm{cos\αe}}^{{\mathrm{i\θ}}_2}+\frac{1}{2}{e}^{-\mathrm{\δ}TE/T_2\left(\stackrel{\→}{r}\right)}\[(1+\cos \mathrm{\α})e^{i({\mathrm{\θ}}_2-{\mathrm{\θ}}_1)}+(1-\cos \mathrm{\α})e^{i({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)}\]\}d\stackrel{\→}{r}$

In formula be spin density distribution, α is the flip angle of excitation pulse, found through experiments, and when α=45 °, the intensity of two echo-signals is all relatively high, δ TE=(TE ₂-TE ₁)/2, wherein δ ₁, δ ₂the persistent period of first and second corresponding respectively echo shift gradient, γ is gyromagnetic ratio; From above formula, in fact have three echo-signals of being modulated by out of phase, wherein Section 1 is produced by second excitation pulse, and then two are produced by first excitation pulse; But will to isolate these three signals relative to the signal that single sweep obtains be very complicated, by analyzing latter two, the echo center of known latter two is different, and last signal intensity is relative to smaller Section 2, therefore last echo can be left in the basket by simple process;

(5) echo-signal that step (4) obtains is separated with following separation algorithm, theoretical according to Fourier transformation, two echo-signals are different in the linear phase of image area, in addition, although two echo-signals cause T2 weighting different due to evolution time difference, they are from same image layer; Therefore, the prior information that the picture structure of both utilizations is similar can combine reconstruction to two echo-signals, and algorithm for reconstructing is as follows:

$\{x_1,x_2\}=\underset{x_1,x_2}{\mathrm{argmin}}\[\left|\right|x_1-x_{10}|{|}_2^2+{\mathrm{\λ}}_1||\▿x_1|{|}_1+{\mathrm{\λ}}_2\left|\right|\▿x_2|{|}_1+{\mathrm{\λ}}_3||\▿(x_1-{\mathrm{\βx}}_2)|{|}_1\]$

Wherein, x ₁, x ₂the image rebuilding out from first and second echo-signal respectively; scale factor, x ₁₀, x ₂₀the initial pictures of first and second echo-signal respectively; λ ₁, λ ₂and λ ₃lagrange's method of multipliers adjustable constraint weight respectively; it is gradient operator; Section 1 is fidelity item, and Section 2 and Section 3 are the sparsity constraints to the first width and the second width image, and last is two width image outline similarity constraint; This two width image has following relation:

Wherein, the linear phase displacement of the first width and the second width image respectively; x ₀being primary signal, is carry out inverse Fourier transform by the primary signal comprising first and second echo-signal to obtain, and solves by iterative algorithm the image that above-mentioned formula just can obtain first after being separated and second echo-signal generation;

(6) image that step (5) is separated carries out T2 imaging calculating; For the T2 formation method of single sweep, the echo time image only needing two width different is just feasible, and the value of T2 is directly tried to achieve by T2 relaxation equation:

$T_2\left(r\right)=\frac{-\mathrm{\Δ}TE}{ln\left(\mathrm{\μ}\frac{S_2\left(\stackrel{\→}{r}\right)}{S_1\left(\stackrel{\→}{r}\right)}\right)},$

Wherein correction factor, Δ TE=TE ₂-TE ₁; S ₁and S ₂the image intensity of first echo-signal and second echo-signal respectively, add full variation (TotalVariation) extrapolation to strengthen the resolution of image, and a setting threshold value, when the numerical value obtained is lower than threshold value, can noise be considered to and be left in the basket, same when the T2 value calculated is excessive, omit; The T2 image of the high-quality with better resolution has been calculated finally by T2 imaging.