基于DWT的图像分块压缩感知重构算法

运用压缩感知理论对大尺寸图像进行重构耗时较长，观测矩阵要求的存储空间较大，且重构后的图像存在明显的块状效应.根据图像小波变换系数的特点，将图像分块思想与DWT变换相结合，提出了一种改进的基于DWT的图像分块压缩感知算法.将图像子块经DWT变换后，保留图像低频系数，只对高频系数进行观测.重构时采用正交匹配追踪算法（OMP）对高频系数进行恢复.Matlab仿真结果表明，新算法跟基于DCT分块压缩感知算法相比，重构图像的PSNR值提高了2~4 dB，重构时间明显减少，与基于二维离散余弦变换(DCT)的分块压缩感知算法相比，块效应有明显的改善，重构图像质量明显提高.

An Improved Image Blocking Compressed Sensing Algorithm Based on DWT

Reconstruction of full image of large size by applying compressed sensing theory requires a long period of time， the observation matrix of linear measurement requires large space，and there is obvious block effect in the reconstructed image.According to the characteristics of the wavelet transformation coefficients of the image，the image block is combined with the DWT transformation,and an improved DWT based image compressed algorithm is proposed.After the DWT transformation，the low frequency coefficients of each image block are preserved，and only the high frequency coefficients are observed.The high frequency coefficients are recovered by the orthogonal matching pursuit algorithm (OMP).Matlab simulation experiment shows that, compared with the non-block compressed sensing algorithm, the algorithm proposed increases the PSNR value of the reconstructed image by 2~4 dB and decreases the reconstructing time significantly; and compared with the two-dimensional discrete cosine transformation (DCT) block compressed sensing algorithm，this algorithm decreases the block effect and improves reconstruction quality significantly.