Fast ℓ1-Minimization Algorithms for Robust Face Recognition

• Published in: IEEE transactions on image processing Vol. 22; no. 7-8; pp. 3234 - 3246
• Main Authors: YANG, Allen Y, ZIHAN ZHOU, ARVIND GANESH BALASUBRAMANIAN, SASTRY, S. Shankar, YI MA
• Format: Journal Article
• Language: English
• Published: New York, NY Institute of Electrical and Electronics Engineers 01.08.2013
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Exact sciences and technology; Face - anatomy & histology; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Information, signal and communications theory; Pattern recognition; Pattern Recognition, Automated - methods; Reproducibility of Results; Robotics - methods; Sampling, quantization; Sensitivity and Specificity; Signal and communications theory; Signal processing; Subtraction Technique; Telecommunications and information theory; Biometrics; Performance evaluation; Scalability; Face recognition; Image processing; Interior point method; Pattern recognition; Convex programming; Implementation; Linear system; ℓ; Message passing; minimization; Homotopy; augmented Lagrangian methods; Illumination; Sparse representation; Fast algorithm; Automatic recognition; Lagrangian method; Compressed sensing
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2013.2262292

l1-minimization refers to finding the minimum l1-norm solution to an underdetermined linear system [Formula: see text]. 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.