外文翻译-- A method for estimating the coil sensitivity maps from the surface images in parallel imaging

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1、A method for estimating the coil sensitivity maps from the surface images in parallel imaging XiaoFang Liu Information technology Institute China Jiliang University Hangzhou china e_mail: YiBing Lao Information technology Institute China Jiliang University Hangzhou china Feng Liu School of Informati

2、on Technology&Electrical Engineering The University of Queensland Brisbane,Qld.4072.,Australia AbstractDerived from the individual surface coil images,a new method based on anisotropic diffusion for estimating the coil sensitivity is proposed in this paper.When the coil sensitivity maps estimated by

3、 this method are applied to reconstruct the magnetic resonance image from the under-sampled images by parallel imaging reconstruction Sensitivity Encoding method,the quality of the reconstructed image is improved.As a result,without using the body coil for additional reference scans,the proposed met

4、hod is valuable for determining the coil sensitivity maps alone from the surface coil images.Keywords-parallel magnetic resonance imaging;coil sensitivity maps;anisotropic diffusion;sensitivity encoding;SENSE I.INTRODUCTION Parallel magnetic resonance imaging(MRI)is one of the modern revolutions in

5、the field of MRI.In parallel imaging,a certain amount of the spatial encoding,traditionally achieved by the phase-encoding gradients,is substituted by evaluating data from several coil elements with spatially different coil sensitivity profiles.However,inaccurate coil sensitivity maps can lead to im

6、age artifacts and a reduction in signal-to-noise(SNR)in the final full Field-Of-View(FOV)reconstructed image1.The standard method for calculating the surface coil sensitivity maps in the image domain was proposed by Pruessmann et al2.This method is based on a special acquisition method designed for

7、coil sensitivity calibration,by which the information from both the surface coils array and the body coil reference image are collected.However,this calibration step can prolong total examination time and partially counteract the benefits of decreased acquisition time associated with parallel MRI.On

8、 the other hand,this method is sensitive to patient motion,and can produce serious errors whenever aliasing is present in the coil sensitivity maps 3.Furthermore,these methods require an intensity threshold and a homogeneous reference image.In recent years,several groups have proposed some other met

9、hods without a separate homogeneous coil image for determining the coil sensitivity maps 45,but they are still sensitive to aliasing the coil images and are computationally slow.It is well-known that the surface coil arrays can potentially increase sensitivity compared to volume coils.Generally,the

10、surface coil sensitivity functions vary slowly as a function of spatial position,and low-resolution in vivo images suffice to form sensitivity reference.In this paper,a new a method for estimating the coil sensitivity map using only post hoc processing of the surface coil image is proposed.The propo

11、sed method doesnt require either a reference image or any prior knowledge about the imaging.In order to evaluate the reliability of the proposed method,the standard Sensitivity Encoding(SENSE)reconstruction method 6 will be applied and a G-factor map depicting the noise added in the unfolding proces

12、s will be generated.II.ANISOTROPIC DIFFUSION MODEL Since the coil sensitivity map consists of the slowly varying sensitivity profile of the coil,it can be acquired by extracting a slowly varying function of position of the coil surface image.The famous anisotropic diffusion scheme proposed by Perona

13、 and Malik 7 can effectively generate the coarser resolution images through a diffusion process of different scale-space,which can be formulated as a partial differential equation(PDE).Given an image I0(x,y),a family of derived images I(x,y;t)of the distinct resolution is obtained by solving an evol

14、ution equation,where the scale-space variable t parameterizes the amount of smoothing,and larger values of t correspond to images at coarser resolutions(,)(,)tIdiv c x y tIc x y tIc I=+i (1)With respect to the scale-space variables t,div denotes the divergence operator.and are respectively the gradi

15、ent and Laplacian operators.c(x,y,t)is the diffusion coefficient.If c(x,y,t)is a constant,(1)reduces to the isotropic heat diffusion equation It=cI.This diffusion must satisfy a certain criteria:causality,piecewise smoothing and immediate localization.A suitable choice of c(x,y,t)determines the reli

16、ability of diffusion.If the edge position in image I(x,y;t)is estimated by gradient of the image,the diffusion coefficient c(x,y,t)should be a function of the magnitude of the gradient as(2):(,)(|(,)|)c x y tfI x y t=(2)978-1-4244-4713-8/10/$25.00 2010 IEEEWhere function f()must be a monotone decrea

17、sing function of the magnitude of the gradient.f()is generally adopted as(3)or(4).2(|/)21(|)(3)(|)(4)|1()I KfIfIeIK=+The scale-spaces generated by these two functions are usually different.However,their experimental results are same in our study.This paper will use(3).In(3)and(4),the constant K shou

18、ld be tuned during the whole anisotropic diffusion.In this paper,the value of K will be determined around the 85%of the absolute value of the gradients of noise samples that are computed using Sobel operator8.III.A NEW NUMERICAL SOLUTION TO ANISOTROPIC DIFFUSION MODEL FOR ESTIMATING THE COIL SENSITI

19、VITY Perona and Malik 7gave an inexact discretization scheme of Eq.(1):1,()ttti ji jNNSSEEWWi jIIcI cI cI cI+=+iiii (5)Here,00.25 for the numerical scheme to be stable,greater results in the faster diffusion,and the symbol indicates the nearest-neighbor differences:,1,S i jiji jIII+，,1,N i jiji jIII

20、,1,E i ji ji jIII+，,1,Wi ji ji jIII (6)Derived from(1),the following nonlinear diffusion model will be used in this paper.()xxyyxxyyIc IIc Ic It=+(7)In consideration of under-sampling on the phase-encoding steps along y-axis direction,the solution to the nonlinear model(7)will be derived as(9)when t

21、he function f()is defined by(3).(1)()()xxyyx xy yI tI tc IIc Ic I+=+(8)(1)()(|)()xxyyI tI tfIII+=+222222(|)(|)()(4)y xxx yyx xxy yyx y xyfIfII II II II II I IKK+(9)IV.EXPERIMENTS AND RESULTS A.MATERIALS The data were acquired from the Martinos Center in MGH9.The original anatomical images were acqui

22、red using a 3T magnetic resonance scanner(Siemens Medical Solutions)with a purpose-built 8-channel 3T head array consisting of a linear array of 9-cmdiameter circular surface coils wrapped around the head.The imaging pulse sequence was a T1-weighted MPRAGE(3D Flash with IR prep)volume exam(TR/TE/TI/

23、flip=2530 ms/3.45 ms/1100 ms/7 degrees),slice thickness=1.33mm,matrix=256256,FOV=256mm.These full FOV images from 8 array surface coils are used to estimate the surface coil sensitivity profiles.For parallel MRI acquisition and reconstruction,Using the same imaging pulse sequence,the surface anatomi

24、cal images were under-sampled in the phase-encoding direction by 50%,40%,33.33%,25%.B.METHODS Parallel MRI uses spatial encoding from multiple radiofrequency detector coils to supplement the phase-encoding supplied by magnetic field gradients,and thereby to accelerate MR image acquisitions.Due to th

25、e reduction in the phase-encoding gradients,the images acquired from array coils are aliased.Using the coil sensitivity maps,these aliased images can be unfolded to reconstruct a full FOV image.It is therefore important to precisely estimate the coil sensitivity maps for parallel imaging.This paper

26、will acquire the coil sensitivity profiles only from the surface coil images by a nonlinear model as(1).In this paper,the multi-scale characteristics of the original surface coil images have been studied by a new numerical scheme of anisotropic diffusion model as(9).During the whole diffusion proces

27、s of the surface coil images,the images at different resolutions are obtained.These derived images will be viewed as the coil sensitivity maps and then utilized to reconstruct full FOV images by the SENSE reconstruction method.This evolution process will end when the mean of the so-called G-factor o

28、ver the reconstructed image begins to increase.At this time,the estimated coil sensitivity maps are complete for reconstructing the full FOV image.However,according to the basic principle of reaching the minimum mean of G-factor of the reconstructed image,it should be noted that the procedure of dif

29、fusion is different for the different speed-up parallel imaging.C.RESULTS Along with this evolution of nonlinear diffusion process,the final coil sensitivity maps of the individual array coils(8-channel)are obtained as shown in Fig 1,which will be used to reconstruct the full FOV image.Figure.1 The

30、coil sensitivity maps of the individual array coils(8-channel,from left to right).These maps will be utilized to reconstruct full FOV image from 2.0-fold under-sampled image.Here the parameter is 0.16 in(9).In this study,when the value of is smaller than 0.12 or greater than 0.20,the results will no

31、t be very good.As shown in Fig.1,these coil sensitivity profiles correlate well to the individual coil locations and the high-sensitivity regions of the anatomical images.Using these coil sensitivity profiles,the reconstructed full FOV images and their G-factor map from 2.0-fold,3.0-fold,3.5-fold an

32、d 4.0-fold,under-sampled image are shown in Fig.2.Figure 2 The reconstructed full FOV image(top)and its G-factor map(bottom).By the standard SENSE method,the reconstructed images(a),(b),(c),(d)are respectively obtained from 2.0-fold,3.0-fold,3.5-fold and 4.0-fold under-sampled images.At the bottom i

33、mages(e),(f),(g),(h),their magnitude and spatial distribution of the noise is shown by G-factor maps.V.DISCUSSION In order to improve the speed in MRI,the k-space data are under-sampled and results in acquiring the aliased images.The coil sensitivity maps make it achievable to unfold these aliased i

34、mages for reconstructing the full FOV image.Because of the incorrectly estimated coil sensitivity functions by the standard method,the reconstructed images exhibit the residual aliasing artifacts.The greater is the reduced number of data readouts,the more are the residual aliasing artifacts in the r

35、econstructed image.From this study,the following aspects can be taken into account when the coil sensitivity maps estimated by our proposed method are used for reconstructing the full FOV image:(1)Because the most reconstruction methods applied with parallel imaging just require the relative sensiti

36、vity differences between the individual receive coils,there is no requirement to determine the absolute coil sensitivity profiles for each coil 10.Therefore according to acceleration factor R,we consider that the coil sensitivity maps can be relatively different for reconstructing the full FOV image

37、.In this study,by controlling the process of nonlinear diffusion of the coil surface images,the different coil sensitivity maps can be obtained.(2)During the anisotropic diffusion of the coil images for estimating the coil sensitivity maps,the mean of the G-factor over the reconstructed image gradua

38、lly changes and moderates at final,which can be shown in Fig.3.Figure 3 The change process of the mean of g-factor over the reconstructed image with the scale-space.The image is reconstructed from the 2.0-fold,3.0-fold,3.5-fold and 4.0-fold aliased images,and the scale-space parameter t varies from

39、3 to 250.In parallel imaging,the price for the shorter acquisition time is the degradation of the SNR in the reconstructed images,and G-factor is generally used to quantify this SNR degradation.When the coil sensitivities are too similar,the matrix inversion used in the reconstruction of the full-FO

40、V image is destabilized and the G-factor arises.In this study,the matrix for reconstructing images has no singular value when the anisotropic diffusion of the original images for estimating the coil sensitivity is at an initial stage,and the G-factor is infinity.As the nonlinear diffusion progresses

41、,the G-factor gradually varies from little to great and then from great to little,and moderates at final.This behavior of the G-factor is similar over the reconstructed image from the different fold under-sampled k-space data.(3)The coil sensitivity map estimated by a nonlinear diffusion of the surf

42、ace coil image can be utilized to reconstruct the full FOV image,but the isolated noise in the reconstructed image can not be eliminated.This isolated noise is likely to improve the G-factor.The P-M model proposed by Perona and Malik can smooth the image and preserve the edge properties well,but the

43、 result of the denoising of isolated noise is not resolved satisfactorily.In order to overcome the drawback of the P-M model,many researchers proposed improvements 11.(4)The proposed method for estimating the coil sensitivity only from the surface coil images presents a tailored method for coil sens

44、itivity calibration for some applications.In general,there are two complementary calibration techniques for acquiring the coil sensitivity profiles:the pre-scan method and the auto-calibration method.These two calibration methods have their own advantages and disadvantages in terms of time efficienc

45、y,user comfort,or robustness of reconstruction.However,they are unsuitable for some applications,while our proposed method can be applied as a coil self-calibration method.For example,the radial sampling schemes and dynamic studies in parallel imaging can be used with our proposed method.(5)The edge

46、 condition for(9)must be cautious.In the study,the edge condition at frequency-encoding steps is different from the edge condition at phase-encoding steps.In consideration of Cartesian sampling,this study sets the edge conditions for(9)along x-direction and along y-direction as(9):00(,)0I x yx=,0000

47、(,)(,)I x yI x yy=(10)Here,I(x0,y0)is the edge pixels of the image I(x,y).The study shows that the edge condition for the gradient of I(x,y)can tremendously affect the coil sensitivity maps.VI.CONCLUSION Parallel magnetic resonance imaging provides a quantum leap in speed for MRI scanners.The most i

48、mportant step in a practical parallel MRI implementation is to acquire the sensitivities of the various coil array elements.In this paper,a new numerical scheme for anisotropic diffusion is proposed to estimate the coil sensitivity maps in the image domain.These maps are directly derived from the in

49、dividual surface coil images.Through the methods proposed and the experimental results presented,the following conclusion can be drawn:(1)Directly from the surface coil imaging data,the coil sensitivity profiles estimated by our proposed method are viable for reconstructing full-FOV images.Since the

50、 slowly varying intensity changes in surface coil image comprise the estimated coil sensitivity map,our method can not only adaptively smooth the anatomical information but also maintain individual coil location and the essential structural information.As a result,the obtained coil sensitivity profi

51、les can provide spatial position information for complementing the absent phase encoding.(2)The proposed algorithm for estimating the coil sensitivity maps doesnt require either a reference image or any prior knowledge about the image.Without using coil position markers and only from the surface coi

52、l inhomogeneous images,the individual coil sensitivity maps can be obtained by a simple nonlinear diffusion of the surface coil images.(3)The study indicates that artifact and noise suppression in the reconstructed image for parallel imaging can be achieved by improving the reliability of the coil s

53、ensitivity maps.In order to improve the quality of the final reconstructed image,the constrained reconstruction is generally shown to be an effective method 121314.However,modifying the values of the coil sensitivities can moderate the ill-conditioning of the matrix inversion for reconstructing imag

54、e.In our study,when the reduced number of data readouts is 4.0,the mean of the g-factor over the reconstructed image decreases from 36.3390 to 26.3260.Therefore,the proposed method is suitable for higher speed-up parallel imaging.REFERENCES 1 F.Huang,Y.Chen,G.R.Duensing,et al,“Application of partial

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