基于近似消息传递的小波域图像压缩感知

Image compressive sensing in wavelet field based on approximate message passing

针对现有的基于近似消息传递的图像压缩感知算法需要构建大尺寸观测矩阵的问题,研究基于近似消息传递的小波域图像压缩感知算法。为了克服逐列观测、逐列重构的传统变换域压缩感知方案隔断图像列与列之间相关性的缺点,提出了一种基于图像行列相关性的小波域压缩观测方案。进而,基于近似消息传递设计了一种适用于在稀疏度未知的情况下重建小波系数的压缩感知重构算法,结合图像小波系数的结构化稀疏特性与近似消息传递,实现了小波域图像压缩感知重构。实验结果表明,与现有算法相比,本文提出的基于图像行列相关性与近似消息传递的小波域图像压缩感知算法具有更高的重建图像质量与更快的图像重建速度。

Since existing image compressive sensing algorithms based on approximate message passing（ AMP） measure the image as a whole,very large measurement matrix would be stored and transmitted. When the coefficient matrix is measured column by column,dependencies among columns would be ignored. Facing these problems,the image compressive sensing algorithm in the wavelet field based on AMP was studied in this paper. A new measurement scheme in the wavelet field based on the dependencies among both columns and rows was proposed. Further,a new scheme was designed to reconstruct wavelet coefficients based on AMP,which does not need the sparsity in advance. Thus,wavelet coefficients of the image are reconstructed based on the spatial correlation and AMP. Simulations results show that,this scheme can achieve higher image reconstruction quality and shorter run time,compared to existing reconstruction schemes in the wavelet field.