Regularization of ill-posed linear inverse problems via l1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an l1â€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2009

We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to theâ€¦ (More)

The problem of assessing the performance of algorithms used for the minimization of an â„“ 1-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion thatâ€¦ (More)

L1Packv2 is a Mathematica package that contains a number of algorithms that can be used for the minimization of an â„“ 1-penalized least squares functional. In particular, an implementation that yieldsâ€¦ (More)

S U M M A R Y We propose the use of 1 regularization in a wavelet basis for the solution of linearized seismic tomography problems Am = d, allowing for the possibility of sharp discontinuitiesâ€¦ (More)

We propose a new gradient projection algorithm that compares favorably with the fastest algorithms available to date for â„“ 1-constrained sparse recovery from noisy data, both in the compressedâ€¦ (More)

Keywords: Inverse problem One-norm Sparsity Tomography Wavelets Regularization a b s t r a c t The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismicâ€¦ (More)