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In this paper, we focus on the least-squares (LS) formulation for the localization problem, where the 12-norm of the residual errors is minimized in a setting known as difference-of-convex-functions programming. The problem at hand is then solved by applying a penalty convex-concave procedure (PCCP) in a successive manner. Algorithmic details that are tailored to the localization problem, such as...
A new algorithm for the reconstruction of sparse signals, which is referred to as the -regularized least squares (-RLS) algorithm, is proposed. The new algorithm is based on the minimization of a smoothed -norm regularized square error with . It uses a conjugate-gradient (CG) optimization method in a sequential minimization strategy that involves a two-parameter continuation...
A new algorithm for the reconstruction of images with sparse gradient is proposed. The algorithm is based on the minimization of the so called total-variation (TV) regularized squared error and is especially suited for image reconstruction from a small number of measurements. The algorithm is developed based on a generalized TV norm and uses a sequential conjugate-gradient method. Simulation results...
A new algorithm for the reconstruction of so called block-sparse signals in a compressive sensing framework is presented. The algorithm is based on minimizing an l2/p-norm regularized l2 error. The minimization is carried out by using a sequential conjugate-gradient algorithm where the line search involved is carried out using a technique based on Banach's fixed-point theorem. Simulation results are...
The basis pursuit denoising refers to the solution of an ℓ1-ℓ2 minimization formulation which is well known as an effective method for signal denoising. In this paper we investigate an ℓp-ℓ2 formulation with p ∈ (0, 1) for denoising. Based on an analysis of the discontinuity of the global minimizer of the ℓp-ℓ2 problem with respect to regularization parameter, we propose two smoothed ℓp-ℓ2 solvers...
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