Sparse Signals and Compressed Sensing

: Compressed sensing arose from the need to process very complex problems in signal and image processing. The idea is to use the image’s original spatial redundancy to extract an image summary containing the patches of texture most representative of the image, then to use this compact representation to reconstruct the initial image. The notion of sparsity has emerged as a fundamental requirement in recent years. A signal is said to be sparse on a basis if it can be described by a low number of non-null coefficients on this basis.