变采样率的磁共振图像分块压缩感知

Block-based compressed sensing for MR image with variable sampling rate

提出一种磁共振(MR)图像的变采样率分块压缩感知(BCS,block-based compressed sensing)方法;根据MR图像细节丰富、纹理复杂的特点,引入对图像高维奇异结构具有良好稀疏表示能力的Tetrolet变换,同时考虑到MR图像各切片间的时空相关性,将相邻时序的MR切片组成图片组(GOP),通过计算参考图片与相邻切片的差异,并对参考图片及差异图进行不重叠分块,根据图像块内容变化的快慢自适应分配采样率,获取测量数据,采用平滑投影Landweber(SPL,smooth projected Landweber)算法实现GOP的高质量压缩感知(CS)重构。实验结果表明,Tetrolet变换适用于MR图像的稀疏表示,相较于采用离散余弦变换(DCT)及双树小波变换(DWT)的方法,本文的重构图像的PSNR平均提高了0.92dB与2.06dB;而且对于不同的GOP,采用变采样率方案时,重构图像的质量均优于固定采样率时所得到的结果,为MR图像的CS提供了一种可行的解决方案。

A block-based compressed sensing scheme for magnetic resonance （MR） image with variable sampling rate is proposed. In view of containing the rich details and complex texture of MR image, the Tetrolet transform,which can represent the high dimensional singularity structure of image sparsely,is introduced. Meanwhile,the adjacent slices of the MR image are bound to constitute a group of pictures （GOP） considering the spatio-temporal correlation between contiguous slices, and the disparities of the reference slice with its immediate previous and following slices are calculated to form the difference images. Then,the reference slice and the difference images are partitioned into the no-overlapped blocks to assign sampling rate according to the changes of contents between sequential image blocks. Finally, COP can be reconstructed from measurements by using the projected Landweber algorithm under the compressed sensing framework. The experimental results show that the Tetrolet transform is a suitable sparse representation tool for MR image. Compared with the methods using discrete cosine transform and dual - tree wavelet transform , the PSNR of the reconstructed images is increased by 0.92 dB and 2.06 dB,averagely. Moreover, for diverse COPs, the qualities of the reconstructed images with variable sampling rate are all better than the results obtained from the fixed sampling rate method. This paper provides a feasible scheme for compressed sensing of MR images.