Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared $\ell_2$) error term combined with a sparseness-inducing ($\ell_1$) regularization term.{\it Basis pursuit}, the {\it least absolute shrinkage and selection operator} (LASSO), … Read more