基于分块压缩感知的图像全局重构模型

已有的基于分块压缩感知（Block Compressed Sensing，Block CS）的图像重构模型采用相同的测量矩阵以块×块的方式获取数据，解决了传统CS方法中测量矩阵所需存储量较大的问题，但由于采用分块重构，没有考虑到图像的全局稀疏度，出现了大量的块效应。本文分析了图像分块重构产生块效应的三个主要原因:块稀疏度不均匀、频谱泄漏和块尺寸受限，提出了一种基于Block CS的图像全局重构模型。该模型在编码端采用高斯随机矩阵逐块作非相关测量；在解码端，引入排序算子，重新构造测量矩阵，该测量矩阵既适合于进行全局重构，又适合于分块测量的CS观测值，并仍与图像的稀疏矩阵高度不相关，所以其可充分利用图像的全局稀疏度进行CS重构。仿真实验表明，所提出的全局重构模型有效地消除了块效应现象，并且对块尺寸的变化有较强的鲁棒性。 

A Global Reconstruction Model of Images Using Block Compressed Sensing

Current image reconstruction models using block compressed sensing (block CS), where data acquisition is conducted in a block-by-block manner through the same measurement matrix, overcomes the difficulties encountered in traditional CS technology of the random measurement ensembles being numerically unwieldy. However, a lot of block artifacts occur in reconstructed images due to the block-by-block manner lack a consideration of global sparsity. This paper analyses three main reasons resulting in block artifacts when image blocks is recovered independently which include nonuniform distribution of block sparsity, spectrum leakage and restricted block size. To resolve them, a new image global model is proposed based on global sparsity. At the encoder, it incoherently measures image block by block using Gaussian random matrix. At the decoder, it introduces reordering operator and reassembles measurement matrix which is not only fit for global reconstruction but also suits CS observed value obtained by measuring image block-by-block. This measurement matrix is still incoherent with sparsity matrix of images, so it can fully utilize global sparsity of images to recovery images by CS algorithms. Experimental results show that the proposed model not only has effectively removed block artifacts, but also has a strong robustness to variable block size.