Image Reconstruction based on Block-based Compressive Sensing

The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signals can be reconstructed accurately using only a small number of basis function coefficients associated with B. A new approach based on Compressive Sensing (CS) framework which is a theory that one may achieve an exact signal reconstruction from sufficient CS measurements taken from a sparse signal is proposed in this paper. Wavelet-based contourlet transform, block-based random Gaussian image sampling matrix and projection-driven compressive sensing recovery are cooperating together in the new process framework to accomplish image reconstruction. Smoothing is achieved via a Wiener filter incorporated into iterative projected Landweber compressive sensing recovery, yielding fast reconstruction. Different kinds of images are tested in this paper, including normal pictures, infrared images, texture images and synthetic aperture radar (SAR) images. The proposed method reconstructs images with quality that matches or exceeds that produced by those popular ones. Also smoothing was imposed with the goal of improving the quality by eliminating blocking artifacts and quality of reconstruction with smoothing is better to that from pursuits-based algorithm.