On some deterministic dictionaries supporting sparsity

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 p unit vectors in a Hilbert space of dimension p, whose pairwise inner products have magnitude of at most 4/ √ p. An explicit algorithm to construct a large portion of the oscillator dictionary is presented.