Adaptive dictionaries for compressive imaging

Compressive imaging reconstructs the original signal by searching through the feasible space for the solution with maximum compactness under a known frame or dictionary. With the extent of available optimization tools, the recovery performance mainly relies on the power of dictionary to sparsely represent the data. Universal dictionaries can be trained from a corpus of natural images or they can be designed through mathematical modeling. However, a problem with universal dictionaries is that they are suboptimal for individual classes of images. To mitigate this suboptimality, we explore ways of adapting the dictionary after the image is sensed using local and non-overlapping sampling matrices. We demonstrate that to prevent the dictionary from becoming biased under the deterministic sensor structure, sampling matrices should have diversity across different locations of the image. The proposed dictionary adaptation along with varying sampling matrices improves the recovery over state-of-the-art universally learned dictionaries of different sizes.