Compressed Sensing for Image Compression: Survey of Algorithms

Compressed sensing (CS) is an image acquisition method, where only few random measurements are taken instead of taking all the necessary samples as suggested by Nyquist sampling theorem. It is one of the most active research areas in the past decade. In this age of digital revolution, where we are dealing with humongous amount of digital data, exploring the concepts of compressed sensing and its applications in the field of image processing is very much relevant and necessary. The paper discusses the basic concepts of compressed sensing and advantages of incorporating CS-based algorithms in image compression. The paper also discusses the drawbacks of CS, and conclusion has been made regarding when the CS-based algorithms are effective and appropriate in image compression applications. As an example, reconstruction of an image acquired in compressed sensing way using \( l_{1} \) minimization, total variation-based augmented Lagrangian method and Bregman method is presented.