Sparse coding from a Bayesian perspective

Sparse coding is a promising theme in computer vision. Most of the existing sparse coding methods are based on either l0 or l1 penalty, which often leads to unstable solution or biased estimation. This is because of the nonconvexity and discontinuity of the l0 penalty and the over-penalization on the true large coefficients of the l1 penalty. In this paper, sparse coding is interpreted from a novel Bayesian perspective, which results in a new objective function through maximum a posteriori estimation. The obtained solution of the objective function can generate more stable results than the l0 penalty and smaller reconstruction errors than the l1 penalty. In addition, the convergence property of the proposed algorithm for sparse coding is also established. The experiments on applications in single image super-resolution and visual tracking demonstrate that the proposed method is more effective than other state-of-the-art methods.