Sparse signal estimation with nonlinear conjugate gradients

Many problems in signal processing involve finding sparse solutions to linear systems of equations. The usual way of achieving this involves minimizing a mixed penalty function composed of a quadratic l₂ term and a sparse inducing l₁ term. Some existing algorithms for minimization include cyclic descent, gradient projection and iterative fixed point methods. Cojugate gradient is well known as a fast algorithm for linear quadratic problems. Here we develop a nonlinear conjugate gradient algorithm for the l₁ penalized least squares problem. This new method uses no line search and is found to be very stable. Description of its performance is provided as well as simulations to demonstrate convergence and comparison to another algorithm.