Abstract :
Compressed sensing is a new paradigm for signal recovery and sampling. It states that a relatively small number of linear measurements of a sparse signal can contain most of its salient information and that the signal can be exactly reconstructed from these highly incomplete observations. The major challenge in practical applications of compressed sensing consists in providing efficient, stable and fast recovery algorithms which, in a few seconds, evaluate a good approximation of a compressible image from highly incomplete and noisy samples.
In this paper, we propose to approach the compressed sensing image recovery problem using adaptive nonlinear filtering strategies in an iterative framework, and we prove the convergence of the resulting two-steps iterative scheme. The results of several numerical experiments confirm that the corresponding algorithm possesses the required properties of efficiency, stability and low computational cost and that its performance is competitive with those of the state of the art algorithms.
In most image reconstruction problems, the images are not directly observable. Instead, one observes a transformed version of the image, possibly corrupted by noise. In the general case, the estimation of the image can be regarded as a simultaneous de-convolution and de-noising problem. Intuitively, a better reconstruction can be obtained by incorporating knowledge of the image into the reconstruction algorithm.
Compressed sensing, also known as compressive sensing, compressive sampling and sparse sampling, is a technique for finding sparse solutions to underdetermined linear systems. In electrical engineering, particularly in signal processing, compressed sensing is the process of acquiring and reconstructing a signal that is supposed to be sparse or compressible.
Compressed Sensing is a new paradigm for signal recovery and sampling. It states that a relatively small number of linear measurements of a sparse signal can contain most of its salient information. It follows that signals that have a sparse representation in a transform domain can be exactly recovered from these measurements by solving an optimization problem