SPGL1 is a solver for large-scale sparse reconstruction problems. For a given noise-level
it can solve (BP)minimizex1subject toAx–b2
Alternatively, it can solve the underdetermined Lasso problem
for a given
. SPGL1 relies only on matrix-vector operations Axand ATyand accepts both explicit matrices, and functions that evaluate these products. In addition, SPGL1 supports the complex-variables case, and solves the true complex one-norm regularized problem.
The support for complex variables is handy in the case of noiselets.
Resource: Rice Compressed Sensing Library.