Learning doubly sparse transforms for image representation

The sparsity of images in a fixed analytic transform domain or dictionary such as DCT or Wavelets has been exploited in many applications in image processing including image compression. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular in image processing. However, the idea of learning sparsifying transforms has received only little attention. We propose a novel problem formulation for learning doubly sparse transforms for signals or image patches. These transforms are a product of a fixed, fast analytic transform such as the DCT, and an adaptive matrix constrained to be sparse. Such transforms can be learnt, stored, and implemented efficiently. We show the superior promise of our approach as compared to analytical sparsifying transforms such as DCT for image representation.