DALM-SVD: Accelerated sparse coding through singular value decomposition of the dictionary

Sparse coding techniques have seen an increasing range of applications in recent years, especially in the area of image processing. In particular, sparse coding using ℓ₁-regularization has been efficiently solved with the Augmented Lagrangian (AL) applied to its dual formulation (DALM). This paper proposes the decomposition of the dictionary matrix in its Singular Value/Vector form in order to simplify and speed-up the implementation of the DALM algorithm. Furthermore, we propose an update rule for the penalty parameter used in AL methods that improves the convergence rate. The SVD of the dictionary matrix is done as a pre-processing step prior to the sparse coding, and thus the method is better suited for applications where the same dictionary is reused for several sparse recovery steps, such as block image processing.