Boosted dictionaries for image restoration based on sparse representations

Sparse representations using learned dictionaries have been successful in several image processing applications. However, using a single dictionary model in inverse problems may lead to instability in estimation. In this paper, we propose to perform image restoration using an ensemble of weak dictionaries that incorporate prior knowledge about the form of linear corruption. The dictionary learned in each round of the training procedure is optimized for the training examples having high reconstruction error in the previous round. The weak dictionaries are either obtained using a weighted K-Means or an example-selection approach. The final restored data is computed as a convex combination of data restored in individual rounds. Results with compressed recovery of standard images show that the proposed dictionaries result in a better performance compared to using a single dictionary obtained with a traditional alternating minimization approach.