Sparse and redundant representations

Compressed-Sensing is a recent branch that separated from sparse and redundant representations, becoming a center of interest of its own. Exploiting sparse representation of signals, their sampling can be made far more eective compared to the classical Nyquist-Shannon sampling. In a recent work that emerged in 2006 by Emmanuel Candes, Justin Romberg, Terence Tao, David Donoho, and others that followed, the theory and practice of this field were beautifully formed, sweeping many researchers and practitioners in excitement. The impact this field has is immense, strengthened by the warm hug by information-theorists, leading mathematicians, and others. So popular has this field become that many confuse it with being the complete story of sparse representation modeling. In this book I discuss the branch of activity on Compressed-Sensing very briefly, and mostly so as to tie it to the more general results known in sparse representation theory. I believe that the accumulated knowledge on compressed-sensing could easily fill a separate book.