The theory and algorithms for many practical problems, ranging from signal and image processing, compressed sensing, statistical regression and computer vision to machine learning, have witnessed significant new developments under the following hypothesis: The unknown data to process is sparse or can be sparsely approximated. Under this fundamental hypothesis, many problems can be formulated as the sparse optimization problem which seeks the sparse solution of an underdetermined linear system or the sparse point in a convex set.
Sparsity has long been exploited in signal and image processing as well as in statistics and learning communities. However, the rapid development in these fields by exploiting sparsity started only around 2004. ...
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