Fast L1-Minimization Algorithms For Robust Face Recognition

TL;DR

This paper introduces fast, scalable L1-minimization algorithms based on Augmented Lagrangian Methods for robust face recognition, significantly improving speed and efficiency in high-dimensional, corrupted facial image classification.

Contribution

The paper develops and validates a new convex optimization solver using ALM for L1-minimization, enhancing scalability and speed over traditional methods in face recognition tasks.

Findings

ALM-based solvers outperform traditional algorithms in speed and scalability.

Extensive experiments validate the effectiveness of the proposed methods.

Publicly available code facilitates peer evaluation and further research.

Abstract

L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In this paper, our study addresses the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from very high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as Augmented Lagrangian Methods (ALM). The new convex solvers provide a viable solution to real-world, time-critical applications such as face recognition. We conduct extensive experiments to validate and compare the performance of the ALM algorithms against several popular L1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing (AMP) and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.