A conjugate subgradient algorithm with adaptive preconditioning for LASSO minimization

TL;DR

This paper introduces a conjugate subgradient algorithm with adaptive preconditioning that efficiently minimizes LASSO problems, significantly reducing iterations needed for ill-conditioned linear inverse problems like computed tomography.

Contribution

It presents a novel conjugate subgradient method with adaptive preconditioning tailored for LASSO minimization, improving convergence speed over existing methods.

Findings

Reduces number of iterations compared to state-of-the-art algorithms.

Effective in solving ill-conditioned linear inverse problems.

Applicable to computed tomography with dictionary learning.

Abstract

This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion of ill-conditioned linear problems, in particular for computed tomography with the dictionary learning method. A comparison with other state-of-art methods shows a significant reduction of the number of iterations, which makes this algorithm appealing for practical use.