Sparse Signal Recovery and Dynamic Update of the Underdetermined System

Sparse signal priors help in a variety of modern signal processing tasks. In many cases, a sparse signal needs to be recovered from an underdetermined system of equations. For instance, sparse approximation of a signal with an overcomplete dictionary or reconstruction of a sparse signal from a small number of linear measurements. The reconstruction problem typically requires solving an l(1) norm minimization problem. In this paper we present homotopy based algorithms to update the solution of some l(1) problems when the system is updated by adding new rows or columns to the underlying system matrix. We also discuss a case where these ideas can be extended to accommodate for more general changes in the system matrix.