Robust sparse coding for face recognition

Recently the sparse representation (or coding) based classification (SRC) has been successfully used in face recognition. In SRC, the testing image is represented as a sparse linear combination of the training samples, and the representation fidelity is measured by the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm or l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm of coding residual. Such a sparse coding model actually assumes that the coding residual follows Gaussian or Laplacian distribution, which may not be accurate enough to describe the coding errors in practice. In this paper, we propose a new scheme, namely the robust sparse coding (RSC), by modeling the sparse coding as a sparsity-constrained robust regression problem. The RSC seeks for the MLE (maximum likelihood estimation) solution of the sparse coding problem, and it is much more robust to outliers (e.g., occlusions, corruptions, etc.) than SRC. An efficient iteratively reweighted sparse coding algorithm is proposed to solve the RSC model. Extensive experiments on representative face databases demonstrate that the RSC scheme is much more effective than state-of-the-art methods in dealing with face occlusion, corruption, lighting and expression changes, etc.