MultiPass lasso algorithms for sparse signal recovery

We develop the MultiPass Lasso (MPL) algorithm for sparse signal recovery. MPL applies the Lasso algorithm in a novel, sequential manner and has the following important attributes. First, MPL improves the estimation of the support of the sparse signal by combining high quality estimates of its partial supports which are sequentially recovered via the Lasso algorithm in each iteration/pass. Second, the algorithm is capable of exploiting the dynamic range in the nonzero magnitudes. Preliminary theoretic analysis shows the potential performance improvement enabled by MPL over Lasso. In addition, we propose the Reweighted MultiPass Lasso algorithm which substitutes Lasso with MPL in each iteration of Reweighted ℓ₁ Minimization. Experimental results favorably support the advantages of the proposed algorithms in both reconstruction accuracy and computational efficiency, thereby supporting the potential of the MultiPass framework for algorithmic development.