Research On Magnetic Resonance Image Reconstruction Based On Compound Sparsity

Magnetic resonance imaging(MRI)is a new medical imaging technique,but its long scanning time has become a problem that must be solved in the development of MRI technology.Compressed sensing method breaks the Nyquist sampling rate,and can use a small amount of sampling data to reconstruct the original signal with large probability.The compressed sensing method provides an effective way to reduce the scanning time of the MRI images.According to the characteristics of MR image that have rich details regions and smooth regions,the prior information is divided into two categories: the sparse prior based on the image patch level and that on the image level.Using the nonlocal similarity of the image,the sparse model of the image patch level can improve the quality of image in smooth and edge regions,and such model is usually regarded as a synthesis sparse model.In the image level,using wavelet coefficients structure sparse characteristics to explore the global correlation of the whole image,also known as the analysis sparse model,it can better preserve the rich details of images.Therefore,based on the compressed sensing framework,by combining these two types of priori information,magnetic resonance image reconstruction based on compound sparsity model is proposed.In the condition of not reducing the quality of image,the amount of data to be sampled is reduced and the scanning time is reduced.This paper mainly contains the following two aspects:Firstly,combining the nonlocal central sparse representation prior information and the high frequency and low frequency of wavelet coefficients sparse representation prior information,the MRI reconstruction model based on the centralize compound sparse representation is proposed.The traditional MRI image reconstruction model contains total variation(TV)regular terms and sparse regular terms of wavelet coefficients.TV operator is a localization operator,which cannot take advantage of the nonlocal correlation in the image,and the wavelet sparse regularization term ignores the sparse structure of the wavelet coefficients.Therefore,in this paper we extract the nonlocal similarity patches on the image,the sparse coefficients are weighted by the sparse coefficients of these similar patches.At the image level,the wavelet coefficients of the low frequency coefficients of the main energy of the image and the high frequency coefficients which describe the detail information of the image are respectively constrained by different norm,which has a great effect on the structure and detail information of the original signal.The experimental results show that the reconstruction quality of the proposed algorithm is higher at the same sampling rate,especially in the low sampling rate.Secondly,aiming at the high and low frequency structure of wavelet and the sparse property of wavelet zero tree structure,combined with nonlocal sparse constraints,two MRI reconstruction models based on low rank compound sparse representation is proposed.The nonlocal central sparse representation is a rough centralized estimation of the sparse coefficients in the image patch layer,so the performance of sparse representation is not high.The nonlocal similar blocks of the image share the same sparse pattern in a transform domain.In other words,the matrices of these similar patches are low rank.So,using the nonlocal low rank sparse representation to estimate the sparsity is more accurately.Wavelet sparse representation described the MRI image in image level,using high frequency and low frequency structure of wavelet coefficients described the distribution of subband coefficients and using zero tree wavelet depicted dependency between different sub bands of wavelet coefficients.Due to the wavelet coefficients structure are divided into two types: overlapping and nonoverlapping.The resulting complex optimization problem is difficult to solve,especially for sparse models with overlapping structures.This paper presents a reasonable solution by combining iterative singular value threshold method and alternating direction multiplier method.The experimental results show that the proposed compound sparse model not only keep a large area smooth but also preserves the rich details and texture of images,and outperform the state-of-the-art CS-MRI reconstruction models in terms of both objective and subjective qualities for MR images.The average of PSNR have 0.5dB and 1.2dB gains respectively.