SparseLab

From SparseSolver

Solver Name SparseLab Authors many Initial release date ? Latest release date ? Solver type Many Problems solved BP, LAG Programming Language Matlab License Free Webpage link

SparseLab from the Donoho Stanford group. Provides many things besides an l1 solver, and has nice tutorial files. One of the original suites of software for compressed sensing. It includes the following solvers:

• Basis pursuit (BP) and LAG form (not BPDN form). Uses the IPM method "PDCO" to solve after recasting BP as LP and BPDN as SOCP.
• Iterative Soft Thresholding (IST), also with block norm variant. Uses path following algorithm, and approximates Least Angle Regression (LARS).
• LAG solver via LARS (w/ or w/o modification). Allows non-negativity constraints.
• Polytope Faces Pursuit algorithm: solves BP via its dual, using Cholesky updates, see M.D. Plumbley paper from 2006.
• Iteratively reweighted least squares (IRLS), using LSQR sub-problem solver.
• Greedy methods: matching pursuit, orthogonal matching pursuit (OMP), forward stepwise regression (w/ and w/o FDR threshold), stagewise orthogonal matchingpursuit (StOMP).