Dual Augmented Lagrangian Method for Efficient Sparse Reconstruction

TL;DR

This paper introduces a dual augmented Lagrangian algorithm tailored for sparse signal reconstruction, excelling in large-scale, poorly conditioned, or dense problem settings by explicitly updating primal variables and leveraging sparsity.

Contribution

It presents a novel dual augmented Lagrangian method that improves efficiency for large-scale sparse reconstruction, especially with dense or poorly conditioned matrices.

Findings

Outperforms existing algorithms on large, dense, or poorly conditioned problems.

Explicit primal updates enhance computational efficiency.

Demonstrates robustness in challenging reconstruction scenarios.

Abstract

We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. Moreover, the primal variable is explicitly updated and the sparsity in the solution is exploited. Numerical comparison with the state-of-the-art algorithms shows that the proposed algorithm is favorable when the design matrix is poorly conditioned or dense and very large.