ABSTRACT
This chapter focuses on solving an under-determined system of linear equations where the solution is known to be sparse. The FOCally Underdetermined System Solver (FOCUSS) technique is generic. It can solve a wide variety of problems arising in sparse recovery. The theory of linear Lagrangian used to derive the FOCUSS algorithm is valid for convex problems, that is, for convex diversity measures. However, FOCUSS is almost always used for solving non-convex diversity measures. The chapter discusses iterative re-weighted least squares techniques as well as the geometrical interpretation behind the majorization-minimization approach. The Split Bregman technique is especially suited for solving unconstrained optimization problems with multiple penalty terms. The chapter illustrates the power of the Split Bregman technique by applying it on a simple problem.
