A PCA-based smoothed projected Landweber algorithm for Block Compressed sensing image reconstruction

This paper presents a smoothed projected Landweber (SPL) algorithm using Principal Component Analysis (PCA) for Block Compressed sensing (BCS). In order to overcome the defect that traditional SPL algorithms using directional transforms are not appropriate for any kind of images on account of their pre-specified property, we fully exploit PCA to train an orthonormal transformation matrix adapted to the content of image, and then use it do hard thresholding to replace the bivariate shrinkage existing in traditional methods. Since the orthonormal transformation matrix is adapted to the content of image, the process of hard thresholding can efficiently reduce noise and enforce the sparsity of image so as to improve the quality of reconstructed image. Experimental results reveal the proposed algorithm outperforms the SPL algorithms using directional transforms in aspect of Peak Signal-to-Noise Ratio (PSNR), although our proposed algorithm is a little slower than them.