Fast ℓ1-minimization and parallelization for face recognition

While ℓ1-minimization (ℓ1-min) has recently been studied extensively in optimization, the high computational cost associated with the traditional algorithms has largely hindered their application to high-dimensional, large-scale problems. This paper discusses accelerated ℓ1-min techniques using augmented Lagrangian methods and its parallelization leveraging the parallelism available in modern GPU and CPU hardware. The performance of the new algorithms is demonstrated in a robust face recognition application. Through extensive simulation and real-world experiments, we provide useful guidelines about applying fast ℓ1-min on large-scale data for practitioners.

[1]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[2]  Allen Y. Yang,et al.  Fast ℓ1-minimization algorithms and an application in robust face recognition: A review , 2010, 2010 IEEE International Conference on Image Processing.

[3]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[4]  John Wright,et al.  Dense Error Correction Via $\ell^1$-Minimization , 2010, IEEE Transactions on Information Theory.

[5]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

[6]  Junfeng Yang,et al.  Alternating Direction Algorithms for 1-Problems in Compressive Sensing , 2009, SIAM J. Sci. Comput..

[7]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[9]  Takeo Kanade,et al.  Multi-PIE , 2008, 2008 8th IEEE International Conference on Automatic Face & Gesture Recognition.

[10]  MaYi,et al.  Dense error correction via l1-minimization , 2010 .

[11]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[12]  Stephen J. Wright,et al.  Sparse Reconstruction by Separable Approximation , 2008, IEEE Transactions on Signal Processing.

[13]  Yaakov Tsaig,et al.  Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse , 2008, IEEE Transactions on Information Theory.

[14]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[15]  Hossein Mobahi,et al.  Toward a Practical Face Recognition System: Robust Alignment and Illumination by Sparse Representation , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[17]  D. Donoho.  For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .

[18]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[19]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.