Modified projected Landweber method for Compressive-Sensing reconstruction of images with non-orthogonal matrices

Compressive Sensing (CS) reconstruction of images using the smoothed projected Landweber (SPL) method is known to achieve excellent performance. However, the complexity of SPL increases for a non-orthogonal measurement matrix. In this paper, we propose a variant of SPL for non-orthogonal matrices without increasing the complexity. In addition, we propose a uniform quantization method for compression of images so as to reduce the communication cost. The performance of the proposed method is comparable to the existing methods for lower measurement rates. This method works particularly well with non-orthogonal random matrices composed of only -1s and +1s.