DENOISING OF NATURAL IMAGES BASED ON COMPRESSIVE SENSING

A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. As a resultof extensive research, today's denoisers can effectively remove large amounts of additive whiteGaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structuredsignal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as it ratively estimating a signal from a perturbed observation. This paper proposes on ways to effectively employ a generic denoiser in a CS reconstruction algorithm. Effectively, this paper gives an overview of the various works developed in CS, including the initial works of convex programming methods and much recently lower cost greedy iterative algorithms. In particular, an extension of the approximate message passing (AMP) framework, called denoising-based AMP (D-AMP), which integrates wide class of denoisers within its iterations, is proposed. From novel theory, this work seeks to demonstrate that, when used with a high performance denoiser for natural images, D-AMP offers an enhanced CS recovery performance while operating tens of times faster than competing methods. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation a teach iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.