Fast ℓ1-minimization algorithms for robust face recognition

Allen Y. Yang, Zihan Zhou, Arvind Ganesh Balasubramanian, S. Shankar Sastry, Yi Ma

Research output: Contribution to journalArticlepeer-review

275 Scopus citations


1-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, we study 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 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. We conduct extensive experiments to validate and compare its performance against several popular ℓ1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing, and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.

Original languageEnglish (US)
Article number6514938
Pages (from-to)3234-3246
Number of pages13
JournalIEEE Transactions on Image Processing
Issue number8
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design


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