Viscosity regularization iterative methods and convergence analysis

Regularization: Convergence of Iterative Half Thresholding Algorithm

In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, Lq regularization with q ∈ (0, 1)) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency. As compared with the convex regularization approaches (say, L1 regularization), however, the convergence issue of the corresponding algorithms are more difficult t...

Scale-space Properties of Nonstationary Iterative Regularization Methods Scale-space Properties of Nonstationary Iterative Regularization Methods

The technical reports of the CVGPR Group are listed under Abstract Most scale-space concepts have been expressed as parabolic or hyperbolic partial diierential equations (PDEs). In this paper we extend our work on scale-space properties of elliptic PDEs arising from regularization methods: we study linear and nonlinear regularization methods that are applied iteratively and with different regul...

Convergence of iterative methods applied to Burgers-Huxley equation

Convergence of the Iterative Methods

In a previous paper, we introduced a coordinate-splitting (CS) form of the equations of motion for multibody systems which together with a modiied nonlinear iteration (CM), is particularly eeective in the solution of certain nonlinear highly oscillatory systems. In this paper, we examine the convergence of the CS and CM iterations and explain the improved convergence of the CM iteration. An exa...

Iterative Projection Methods for Structured Sparsity Regularization

In this paper we propose a general framework to characterize and solve the optimization problems underlying a large class of sparsity based regularization algorithms. More precisely, we study the minimization of learning functionals that are sums of a differentiable data term and a convex non differentiable penalty. These latter penalties have recently become popular in machine learning since t...