An Iterative Weighing Algorithm for Image Reconstruction in Compressive Sensing

Compressive sensing (CS), is a framework which points us a promising way of not measuring N-dimensional signals directly, but rather a set of related measurements, which a linear combination of the original underlying N-dimensional signal. However, the traditional CS reconstruction methods use l1-norm optimization which usually gives poor performance on 2D signal or only suit for specific natural image. In this paper, an iterative weighing algorithm for image reconstruction in CS is proposed. According to the sparsity of last iteration, the algorithm iteratively refines the weighting coefficients to enhance the sparsity of the reconstruction results until the convergence is reached. The experiments for natural image and remote sensing image demonstrate that the proposed method can outperforms the traditional CS framework in image reconstruction in the sense that the PSNR of reconstruction image improve over 2dB in the average.