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.