À¶Ý®ÊÓƵ

The area of sparse representation of signals is drawing tremendous attention in recent years in diverse fields of science and engineering. The ideaÌýbehind the model is that a signal can be approximated as a linear

combination of a few "atoms'' from a pre-specified and over-complete

"dictionary'' (typically represented by columns from a matrix with more

columns than rows). The sparse representation of a signal is often achievedÌýby minimizing anÌýL¹Ìýpenalized least squares functional. Various

iterative-shrinkage algorithms have recently been developed and are quiteÌýeffective for handling these problems, often surpassing traditional

optimization techniques. Here we suggest a new iterative multilevel approachÌýthat reduces the computational cost of existing solvers for these inverseÌýproblems. Our method takes advantage of the typically sparse representationÌýof the signal, and, at each iteration, it adaptively creates and processes aÌýhierarchy of lower-dimensional problems employing well-known iteratedÌýshrinkage methods. Analytical observations suggest, and numerical resultsÌýconfirm, that this new approach may significantly enhance the performance ofÌýexisting iterative shrinkage algorithms in cases where the dictionary is anÌýexplicit matrix.

(This is joint work with Eran Treister.)