利用压缩感知理论对图像进行测量和重构时,基于分块思想可有效提高重构速度,但同时会带来较强的块效应。为了解决该问题,在编码端提出了一种基于边缘检测的自适应分块压缩感知测量方案;在解码端提出了一种基于主成分分析(PCA)的平滑投影Landweber(SPL)重构法,该算法运用PCA训练出适合于图像结构的稀疏字典,用于进行硬阈值收缩,从而有效消除了块效应,提升了重构图像的质量。为了提高硬阈值收缩效率和减少训练复杂度,采用了3种基于块的PCA硬阈值收缩方案:全局PCA、局部PCA和分层PCA。仿真实验结果表明:所提出的自适应压缩感知测量方案与SPL重构法相结合,和传统分块压缩感知方案相比,峰值信噪比(PSNR)值均提升了13 dB;本文算法,无论在传统分块压缩感知方案下还是在自适应分块压缩感知方案下,与基于方向小波阈值收缩的SPL重构算法相比,均获得了更高的PSNR值。

While using compressed sensing to measure and recover images, the approach to divide an image into blocks may improve the speed of reconstruction but will bring strong blocking effects. In order to solve this problem, we propose an adaptive block compressed sensing based on edge detection at the encoder, and a smoothed projected Landweber(SPL) reconstruction algorithm based on principal components analysis(PCA) at the decoder. The reconstruction algorithm uses PCA to train a dictionary adapting to image structure using hard thresholding, thus the image blocking effects are eliminated effectively and the reconstructed image quality is improved. In order to improve the efficiency of the hard thresholding and to reduce the training complexity, three hard thresholding schemes using patch based PCA are proposed: global PCA, local PCA, and hierarchical PCA. As a comparison between our experimental results and the traditional block compressed sen- sing shows, the peak signal-to-noise ratio(PSNR) of the recovered images using the SPL reconstruction algorithms combined with the adaptive block compressed sensing is improved by 13 dB; Regardless of which method is being used at the encoder, the SPL reconstruction algorithms using PCA based hard thresholding are better than SPL algorithms using directional wavelet based thresholding on PSNR.