On some deterministic dictionaries supporting sparsity
Shamgar Gurevich (UC Berkeley), Ronny Hadani (University of Chicago),, Nir Sochen (Tel Aviv University)

TL;DR
This paper introduces the oscillator dictionary, a new deterministic incoherent dictionary based on finite group representations, supporting sparse representations with low mutual coherence.
Contribution
It presents a novel construction of an incoherent dictionary using finite group theory and provides an explicit algorithm for generating a large subset.
Findings
Dictionary size of p^5 vectors in p-dimensional space
Maximum inner product magnitude of 4/√p
Explicit construction algorithm provided
Abstract
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 order of p^5 unit vectors in a Hilbert space of dimension p, where p is an odd prime, 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Mathematical Analysis and Transform Methods · Sparse and Compressive Sensing Techniques
