Blind Compressed Sensing Over a Structured Union of Subspaces

Understand

This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements.

• Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals come from a union of a small number of disjoint subspaces.
• This problem is important, for instance, in image inpainting applications, in which the multiple signals are constituted by (incomplete) image patches taken from the overall image.
• This work extends standard dictionary learning and block-sparse dictionary optimization, by considering compressive measurements, e.g., incomplete data).