Compressive dictionary learning for image recovery

In this paper, we tackle real-time learning of a dictionary D from compressive measurements Y of an image X. Existing dictionary learning algorithms are inapplicable because compressive samples Y = ΦX are incomplete and can be arbitrary linear combinations of different pixels. Our strategy is to learn a dictionary of the form D = ΨΘ, which represents compressible dictionaries with respect to the base dictionary Ψ. We show that our method for learning dictionaries during compressive image recovery can improve the recovery results by up to 3 dBs for general random sampling matrices.