We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups. The oscillator dictionary consists of approximately p5 unit vectors in a Hilbert space of dimension p, whose pairwise inner products have magnitude of at most \(4/\sqrt{p}\) . An explicit algorithm to construct a large portion of the oscillator dictionary is presented.
['Shamgar Gurevich', 'Ronny Hadani', 'Nir A. Sochen']
On some deterministic dictionaries supporting sparsity