A Survey of Compressive Sensing Based Greedy Pursuit Reconstruction Algorithms

Conventional approaches to sampling images use Shannon theorem, which requires signals to be sampled at a rate twice the maximum frequency. This criterion leads to larger storage and bandwidth requirements. Compressive Sensing (CS) is a novel sampling technique that removes the bottleneck imposed by Shannon's theorem. This theory utilizes sparsity present in the images to recover it from fewer observations than the traditional methods. It joins the sampling and compression steps and enables to reconstruct with the only fewer number of observations. This property of compressive Sensing provides evident advantages over Nyquist-Shannon theorem. The image reconstruction algorithms with CS increase the efficiency of the overall algorithm in reconstructing the sparse signal. There are various algorithms available for recovery. These algorithms include convex minimization class, greedy pursuit algorithms. Numerous algorithms come under these classes of recovery techniques. This paper discusses the origin, purpose, scope and implementation of CS in image reconstruction. It also depicts various reconstruction algorithms and compares their complexity, PSNR and running time. It concludes with the discussion of the various versions of these reconstruction algorithms and future direction of CS-based image reconstruction algorithms.