CN106199473A - A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted - Google Patents

Abstract

The invention discloses a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, comprise the following steps: to set up model of fit by many b value weighted datas；Signal to noise ratio is estimated by many b value weighted datas；According to signal-to-noise ratio computation residual GM weights α_i, set up model of fit initial value；According to residual GM weights α_iDigital simulation model residual GM value；If model of fit residual GM value meets the condition of convergence, then calculated by the optimal solution of model of fit and improve its stability；Otherwise, return step 4 and continue to look for the optimal solution of model of fit, the method is for many b values diffusion-weighted structure model of fit, improve model optimizing by the optimization of least-squares algorithm and seek stability of solution, and then make the estimation of parametric image in MRI imaging more stable, reduce singular value or the appearance of meaningless values, promote development and the application of MRI imaging technique further.

Description

A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted

Technical field

The present invention relates to the Optimal improvements method of Nonlinear Least-Square Algorithm in the application of a kind of MRI imaging technique, especially Relate to a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted.

Background technology

Diffusion magnetic resonance imaging techniques based on many weighting b values increasingly become the development trend of diffusion magnetic resonance technology, Including diffusion kurtosis imaging, diffusion spectrum imaging etc..Meanwhile, the exponent number of model is also improving constantly, such as, open from the diffusion of second order Amount is imaged onto the diffusion kurtosis imaging model of quadravalence.Thus the sensitivity for data SNR of model is more sensitive, Thus in actual applications, due to the error of models fitting occur that singular value, matching be unstable, the situation of meaningless solution the most gradually Increase, the stable performance of influence technique and application.This technological invention is intended to, by certain algorithm improvement optimization, improve many b values The optimizing of model solves stability, promotes development and the application of MRI imaging technique further.

Summary of the invention

The technical problem existed for prior art, the present invention provides a kind of many b values based on noise Ratio Weighted to spread magnetic Resonance image-forming optimization method, the method is for many b values diffusion-weighted structure model of fit, by the optimization of least-squares algorithm Improve model optimizing and seek stability of solution, and then make the estimation of parametric image in MRI imaging more stable, reduce singular value or The appearance of meaningless values, promotes development and the application of MRI imaging technique further.

In order to solve to exist in prior art technical problem, the present invention uses following steps to be practiced:

A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, comprise the following steps:

Step one, sets up model of fit by many b value weighted datas；

Step 2, estimates signal to noise ratio by many b value weighted datas；

Step 3, according to signal-to-noise ratio computation residual GM weights α_i,

Step 4, sets up model of fit initial value；

Step 5, according to residual GM weights α_iDigital simulation model residual GM value；

Step 6, if model of fit residual GM value meets the condition of convergence, is then calculated by the optimal solution of model of fit Improve its stability；Otherwise, return step 4 and continue to look for the optimal solution of model of fit.

Model of fit in described step one sets up S_i=f (b_i, β), wherein β is unknown parameter to be solved, S_i> 0, i =0,1,2,3 ...；b₀=0；Bi > 0, i=1,2,3 ....

In described step 2, the estimation of signal to noise ratio is to include overall situation signal to noise ratio and local SNR, i.e. SNR_iAnd SNR₀。

Residual GM weights α in described step 3_iEmploying equation below:

Here, b₀=0；b_i> 0, i=1,2,3 ...., b_iOften value 500,1000,1500,2000,2500 ....

In described step 5, model of fit residual GM value calculates and uses equation below:

$E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)}^2.$

In described step 6, model of fit optimal solution calculates and uses equation below:

$\begin{array}{cc}\min .& E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)}^2\end{array}.$

The method have the benefit that

First, the present invention, by estimating the noise Ratio Weighted of different weights b Value Data, cuts down or eliminates different weights b Value signal to noise ratio difference, and then reduce the impact on models fitting stability of noise and error of fitting.

Second, as in figure 2 it is shown, residual sum of squares (RSS) is modified by the present invention by introducing in model optimization solution procedure Weight vector so that the parametric results of curve matching relys more on the weighting b value of high s/n ratio, the i.e. higher noise of limited guarantee The ratio b value point data of (relatively low), thus reduce the noise impact on curve matching in high b value so that solving of parameter is more steady Fixed.

3rd, as it is shown on figure 3, the situation of singular value occurs in grey matter and grey matter regions more, the present invention is by the highest Grey matter white matter kurtosis value is estimated lower value even null value.Provide the inventive method the most respectively to grey matter (Fig. 4), white matter (figure 5) singular value and the effect of normal (Fig. 6) tissue.E and Ec in Fig. 4, Fig. 5 and Fig. 6, is the solved function before revising respectively Curved surface (formula 5) and revised solved function curved surface (formula 6), white in figure "+" it is the position of the solution that two kinds of methods obtain；Phase Ying Di, in figure, lower section gives the matched curve that distinct methods obtains, and wherein blueness is the song using the inventive method to obtain Line fitting result.This three figures result substantially illustrates the effect of the inventive method: can solve appearance in fit procedure very well Singular value phenomenon, does not affect the most stable fitting result simultaneously.

4th, as it is shown in fig. 7, give existing method and the knot of diffusion kurtosis imaging parameters figure that the inventive method obtains Really, wherein top two figures are the Parameter Map that existing method obtains, and two figures of lower section are the Parameter Map using the inventive method to obtain.

Accompanying drawing explanation

Fig. 1 is a kind of many b value diffusion magnetic resonance imaging optimization method flow charts based on noise Ratio Weighted of the present invention.

Fig. 2 be a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted of the present invention to residual error and Fitting result affect figure.

Fig. 3 is the models fitting of a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted of the present invention Singular value signal (stain) figure that result easily occurs.

Fig. 4 is grey matter or the brain of a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted of the present invention The singular value figure of spinal fluid.

The white matter position of a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted of Fig. 5 present invention is strange Different value figure.

Fig. 6 is the prioritization scheme of a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted of the present invention Figure to normal portions.

Fig. 7 is the prioritization scheme of a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted of the present invention Actual effect show that figure is (left: average kurtosis；Right: radially kurtosis).

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is made and explaining:

As it is shown in figure 1, the present invention provides a kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, Comprise the following steps:

Step one 101, sets up model of fit by many b value weighted datas；Model of fit in described step one sets up S_i =f (b_i, β), wherein β is unknown parameter to be solved, S_i> 0, b_i> 0, i=0,1,2,3 ....

In practice, many b value weighted imagings are the most relatively conventional in current MRI technique application, and its data include one Individual b=0 without the Diffusion-Weighted MR Imaging signal (image) under diffusion-weighted reference signal (image), and some non-zero b values, and The diffusion-weighted signal of these non-zeros b value (image) is from same object.Here setting reference signal as intensity is S₀=S (b₀), and The signal of weighting b value is S_i=S (b_i) (i=1,2,3 ...).For certain object, (imitative body material object, animals and plants etc. are all nonmetal Thing) when carrying out many b value Diffusion-Weighted MR Imagings, the intensity of signal S reduces greatly and constantly along with b value becomes, and the curve of composition is referred to as Attenuation curve, is fitted with different models and the architectural characteristic of quantitative description object in actual application.Here by all moulds Use S to type general abstract_i=f (b_i, β) represent, wherein β is unknown parameter to be solved, S_i> 0, b_i> 0, i=0,1,2,3 ....

Step 2 102, estimates signal to noise ratio by many b value weighted datas；In described step 2, the estimation of signal to noise ratio is to include Overall situation signal to noise ratio and local SNR, i.e. SNR_iAnd SNR₀.Need exist for explanation, in identical machine environment, different b value numbers It is identical according to the level of noise in (signal or image), and the signal intensity difference obtained due to different b value weightings so that no Signal to noise ratio with b value weighted data is different.Need exist for first estimating the signal to noise ratio of different b value weighted image, including overall situation letter Make an uproar than and local SNR.Wherein, overall situation signal to noise ratio snr_i=MeanSignal/MeanNoise.Here MeanSignal is The average of signal (detection object or the signal of target area) in i b value image, MeanNoise is i-th b value image hollow The average of gas noise signal (non-detection object or the signal of nontarget area).Local SNR SNR_iBy local space (or Regional area/the neighborhood of person's image) average of signal estimates divided by the standard deviation of signal.

Step 3 103, according to signal-to-noise ratio computation residual GM weights α_i, residual GM weights α in described step 3_iUse Equation below:

Here, b₀=0；b_i＞ 0.i=1,2,3 ..., b_iOften value 500,1000,1500,2000,2500 ... (1)

Fitting precision in data and curves depends on the reliability of sampled point (known point) data to a certain extent.Because no Different with its signal to noise ratio of signal obtained under weighting b value, thus wherein the credibility of useful signal or data is the most different, The matching of curve or this model can be caused certain deviation by this.Specifically, the incoordinate signal to noise ratio of sampled point makes noise Impact on curve fitting precision is more notable, wants to control this impact, it is necessary first to according under signal-to-noise ratio (SNR) estimation difference b value The degree of reliability of signal.

Step 4 104, sets up model of fit initial value；It is to certain occurrence of β in model of fit(initial value), adopts Calculate by equation below:

$S_i=f(b_i,\widehat{\mathrm{\β}})+\mathrm{\μ}---\left(2\right)$

Its residual sum of squares (RSS) is:

$E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)}^2---\left(3\right)$

Step 5 105, according to residual GM weights α_iDigital simulation model residual GM value；Matching mould in described step 5 Type residual GM value calculates and uses equation below:

$E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)}^2.---\left(4\right)$

Step 6 (106,107), if model of fit residual GM value meets the condition of convergence, then by model of fit Excellent solution calculates its stability of raising；Otherwise, return step 4 and continue to look for the optimal solution of model of fit.

In described step 6, model of fit optimal solution calculates and uses equation below:

$\begin{array}{cc}\min & E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)}^2\end{array}.---\left(5\right)$

The first-order condition of upper formula minimalization:

$\frac{dE\left(\widehat{\mathrm{\β}}\right)}{d\widehat{\mathrm{\β}}}=-2{\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\×(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)\×\left(\frac{-df(b_i,\widehat{\mathrm{\β}})}{d\widehat{\mathrm{\β}}}\right)=0---\left(6\right)$

Not having any impact for the process and method finding optimal solution before and after introducing weights, simply residual sum of squares (RSS) occurs Change, be the position of optimal solution there occurs change for image.The residual sum of squares (RSS) improved is by weights such as each points Cumulative, and the weighted sum of squares that residual sum of squares (RSS) is difference estimation difference after improving, therefore new at this residual sum function On seek optimal solution.Especially, the dimension of this residual sum function is consistent with the number of the location parameter of β.If β has two unknown ginsengs Number, the latitude of residual sum function is 2, is a quadratic surface；And the minimum first-order condition of residual error function also will become two Single order partially leads vertical equal to zero.

In the present invention, model of fit seeks the process of optimal solution return step 4 is by iteration optimization method, wherein with β =(β₀, β₁As a example by),

The first-order condition of minimalization is:

$\frac{dE({\mathrm{\β}}_0,{\mathrm{\β}}_1)}{{\mathrm{d\β}}_0}=-2{\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\×(S_i-f(b_i,{\mathrm{\β}}_0,{\mathrm{\β}}_1\left)\right)\×\left(\frac{-df(b_i,{\mathrm{\β}}_0,{\mathrm{\β}}_1)}{{\mathrm{d\β}}_1}\right)=0---\left(7\right)$

$\frac{dE({\mathrm{\β}}_0,{\mathrm{\β}}_1)}{{\mathrm{d\β}}_1}=-2{\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\×(S_i-f(b_i,{\mathrm{\β}}_0,{\mathrm{\β}}_1\left)\right)\×\left(\frac{-df(b_i,{\mathrm{\β}}_0,{\mathrm{\β}}_1)}{{\mathrm{d\β}}_1}\right)=0---\left(8\right)$

In diffusion magnetic resonance technology, the diffusive attenuation model of many b values mostly is nonlinear, such as conic section or double index Curve etc., thus substantially use the solution throughway of non-linear least square.In concrete practice, also can add some and the unknown is joined The constraints of number, and use the solution procedure that some are different, the most also it is the variant of non-linear least square.Non-linear minimum The thinking of square law is, by Taylor series, mean value function is expanded into linear model.That is, single order expansion, high-order are only included Expansion is all included into error term.Carry out OLS recurrence the most again, using the estimator that obtains as new breaking up point, to linear portion Divide and estimate.And so forth, until restraining.Here Gauss-Newton (Gauss-Newton) solution by iterative method is given non-linear The numerical solution process of least square problem.

Archetype is launched Taylor series, takes first approximation value:

$f(b_i,\widehat{\mathrm{\β}})\≈f(b_i,{\widehat{\mathrm{\β}}}_{\left(0\right)})+\frac{df(b_i,\widehat{\mathrm{\β}})}{d\widehat{\mathrm{\β}}}{|}_{{\widehat{\mathrm{\β}}}_{\left(0\right)}}(\widehat{\mathrm{\β}}-{\widehat{\mathrm{\β}}}_{\left(0\right)})---\left(9\right)$

$z_i\left(\widehat{\mathrm{\β}}\right)=\frac{df(b_i,\widehat{\mathrm{\β}})}{d\widehat{\mathrm{\β}}}---\left(10\right)$

$\begin{array}{c}E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}})-z_i({\widehat{\mathrm{\β}}}_{\left(0\right)}\left)\right(\widehat{\mathrm{\β}}-{\widehat{\mathrm{\β}}}_{\left(0\right)}\left)\right)}^2\\ ={\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}})+z_i({\widehat{\mathrm{\β}}}_{\left(0\right)}){\widehat{\mathrm{\β}}}_{\left(0\right)}-z_i({\widehat{\mathrm{\β}}}_{\left(0\right)}\left)\widehat{\mathrm{\β}}\right)}^2\\ ={\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\×{\left(\widetilde{S_t}\right({\widehat{\mathrm{\β}}}_{\left(0\right)})-z_i({\widehat{\mathrm{\β}}}_{\left(0\right)}\left)\widehat{\mathrm{\β}}\right)}^2\end{array}---\left(11\right)$

Construct and estimate linear pseudomodel:

$\widetilde{S_t}\left({\widehat{\mathrm{\β}}}_{\left(0\right)}\right)=z_i\left({\widehat{\mathrm{\β}}}_{\left(0\right)}\right)\widehat{\mathrm{\β}}+{\mathrm{\ϵ}}_{{}_i}---\left(12\right)$

$\widetilde{E_t}\left({\widehat{\mathrm{\β}}}_{\left(1\right)}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{\left(\widetilde{S_t}\right({\widehat{\mathrm{\β}}}_{\left(0\right)})-z_i({\widehat{\mathrm{\β}}}_{\left(0\right)}\left){\widehat{\mathrm{\β}}}_{\left(1\right)}\right)}^2---\left(13\right)$

Estimate to obtain iterative value for the first timeAnd continue iteration.Complete iterative process as follows:

The first step: provide estimates of parametersInitial valueWill?Place launches Taylor series, takes single order Approximation；

Second step: calculateWithSample observations；

3rd step: use common Least Square Method modelObtain the estimated value of β

4th step: useReplace in the first stepRepeat these processes, until convergence.

The condition of convergence be set with bigger degree of freedom, be such as set to 100 subsequent iteration residual errors equal to 0 or constant It is believed that convergence.

The inventive method is to try hard to solve in diffusion magnetic resonance imaging many b value model fitting problems, and different b value signal to noise ratios are not With the lowest problem that models fitting result precision and stability is damaged of the highest b value signal to noise ratio.In applying with reality As a example by diffusion kurtosis imaging (diffusion kurtosis imaging, DKI) model, its fitting function is:

f(b_i, β) and=-b_i×D+(1/6)×(b_i×D)²×K

=-b_i×D+(1/6)×b_i ²×D×K

Here β=[D K].Therefore this Solve problems is the function (formula 5,6) of 2 parameters, and its problem is at one two Minima is asked for, such as E and Ec in Fig. 3,4,5 on dimension curved surface.Owing to K is a Fourth amount, to the noise in model and Error quite sensitive, thus singular value point as shown in Figure 2 easily occurs.Fig. 4, in 5, it can be seen that the solution place of solved function Scope is bigger at the dimension upper span of K, more embodies error of fitting unstability in K value is estimated.And the inventive method exists Purpose in DKI application is exactly to solve the instability problem that kurtosis is estimated by DKI.DKI uses in application at least to be needed much In the non-zero b values of 2, (b value magnitude is 10³, unit is s/mm²), and wherein must have the high b value being not less than b=2000, this In, high b value will introduce the match point of relatively low signal-to-noise ratio, affects the estimation of kurtosis.The inventive method is used to be obviously improved The kurtosis improving DKI model is estimated, as shown in Figure 6.

Examples detailed above is merely to illustrate the present invention, and the structure of the most each parts, material, connected mode are all to have become Change, every equivalents carried out on the basis of the technology of the present invention and improvement, the most should not get rid of the protection model in the present invention Outside enclosing.

Claims (6)

1. many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, it is characterised in that include following step Rapid:

Step one, sets up model of fit by many b value weighted datas；

Step 2, estimates signal to noise ratio by many b value weighted datas；

Step 3, according to signal-to-noise ratio computation residual GM weights α_i,

Step 4, sets up model of fit initial value；

Step 5, according to residual GM weights α_iDigital simulation model residual GM value；

Step 6, if model of fit residual GM value meets the condition of convergence, is then calculated by the optimal solution of model of fit and improves Its stability；Otherwise, return step 4 and continue to look for the optimal solution of model of fit.

A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, its feature Being, the model of fit in described step one sets up S_i=f (b_i, β), wherein β is unknown parameter to be solved, S_i> 0, i=0, 1,2,3…；b₀=0；b_i> 0, i=1,2,3 ....

A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, its feature Being, in described step 2, the estimation of signal to noise ratio is to include overall situation signal to noise ratio and local SNR, i.e. SNR_iAnd SNR₀。

A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, its feature It is, residual GM weights α in described step 3_iEmploying equation below:

Here, b₀=0；b_i> 0, i=1,2,3 ...., b_iOften value 500,1000,1500,2000,2500 ....

A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, its feature Being, in described step 5, model of fit residual GM value calculates and uses equation below:

$E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)}^2.$

A kind of many b value diffusion magnetic resonance imaging optimization methods based on noise Ratio Weighted, its feature Being, in described step 6, model of fit optimal solution calculates and uses equation below:

$\begin{array}{cc}\min .& E\left(\widehat{\mathrm{\β}}\right)={\mathrm{\Σ}}_{i=0}^n{\mathrm{\α}}_i\×{(S_i-f(b_i,\widehat{\mathrm{\β}}\left)\right)}^2.\end{array}$