This package has solvers for constrained and unconstrained L1 minimization, which is useful for compressed sensing.
u = COORDL1BREG(A,f,lambda) solves the minimization problem
min_u ||u||_1 subject to A*u = f
where A is an MxN matrix and f is a vector of length M. Input lambda is a positive parameter used within the algorithm.
u = COORDLSL1(A,f,lambda) solves the minimization problem
min_u ||u||_1 + lambda ||A*u - f||_2^2
Algorithms are based on greedy coordinate descent and the Bregman iterative method.