Path-Based Dictionary Augmentation: A Framework for Improving k-Sparse Image Processing.

We have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved k-sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a "path," or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries.