INTRODUCTION: Compressed Sensing (CS) ([1], [2], [3], [4]) allows reconstructing a signal, if it can be represented sparsely in a suitable basis [4], from only a portion of its Fourier coefficients. It was first used by Lustig et al. [5] in MRI, and it has become popular for speeding up the acquisition process. Initially, CS was introduced as an l0-norm minimization [1] which is in practice uns...

Least Squares Support Vector Machines (LSSVM) perform classification using L2-norm on the weight vector and a squared loss function with linear constraints. The major advantage over classical L2-norm support vector machine (SVM) is that it solves a system of linear equations rather than solving a quadratic programming problem. The L2norm penalty on the weight vectors is known to robustly select...

The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops new L0-norm regularization approach to the convex quantile and expectile regressions for subset selection. We show how use mixed-integer programming solve proposed practice build link commonly used L1-norm approach. A Monte Carlo study performed compare finite sample performances L0-penalized ...

Least-Squares Support Vector Machines (LS-SVMs) have been successfully applied in many classification and regression tasks. Their main drawback is the lack of sparseness of the final models. Thus, a procedure to sparsify LS-SVMs is a frequent desideratum. In this paper, we adapt to the LS-SVM case a recent work for sparsifying classical SVM classifiers, which is based on an iterative approximat...

INTRODUCTION Both L1 minimization [1] and homotopic L0 minimization [2] techniques have shown success in compressed-sensing MRI reconstruction using reduced k-space data. L1 minimization algorithm is known to usually shrink the magnitude of reconstructions especially for larger coefficients [1, 3] and non-convex penalty used in homotopic L0 minimization is advocated to replace L1 penalty [3]. H...

Least mean square (LMS) based adaptive algorithms have been attracted much attention since their low computational complexity and robust recovery capability. To exploit the channel sparsity, LMS-based adaptive sparse channel estimation methods, e.g., L1-norm LMS or zero-attracting LMS (sparse LMS or ZA-LMS), reweighted zero attracting LMS (RZA-LMS) and Lp-norm LMS (LP-LMS), have been proposed b...

INTRODUCTION Both L1 minimization [1] and homotopic L0 minimization [2] techniques have shown success in compressed-sensing MRI reconstruction using reduced k-space data. L1 minimization algorithm is known to usually shrink the magnitude of reconstructions especially for larger coefficients [1, 3] and non-convex penalty used in homotopic L0 minimization is advocated to replace L1 penalty [3]. H...

In this paper we consider general l0-norm minimization problems, that is, the problems with l0-norm appearing in either objective function or constraint. In particular, we first reformulate the l0-norm constrained problem as an equivalent rank minimization problem and then apply the penalty decomposition (PD) method proposed in [33] to solve the latter problem. By utilizing the special structur...

The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops new L0-norm regularization approach to the convex quantile and expectile regressions for subset selection. We show how use mixed-integer programming solve proposed practice build link commonly used L1-norm approach. A Monte Carlo study performed compare finite sample performances L0-penalized ...