A Wide-Angle View of Iterated Shrinkage Algorithms For Finding Sparse Representations
August 26th, 2007
SPIE, Wavelet XII, san-Diego, CA. A plenary talk.

Modeling of signals or images by a sparse and redundant representation is shown in recent years to be very effective, often leading to stat-of-the-art results in many applications. Applications leaning on this model can be cast as energy minimization problems, where the unknown is a high-dimensional and very sparse vector. Surprisingly, traditional tools in optimization, including very recently developed interior-point algorithms, tend to perform very poorly on these problems. A recently emerging alternative is a family of techniques, known as “iterated-shrinkage” methods. There are various and different such algorithms, but common to them all is the fact that each of their iterations require a simple forward and inverse transform (e.g. wavelet), and a scalar shrinkage look-up-table (LUT) step. In this talk we shall explain the need for such algorithms, present some of them, and show how they perform on a classic image deblurring problem.

Joint work with Boaz Matalon, Michael Zibulevsky, and Joseph Shtok.