Super-Resolution of Mutually Interfering Signals

TL;DR

This paper introduces a convex programming algorithm for super-resolution of overlapping signals from different sources, with theoretical guarantees and numerical validation, applicable in imaging, neural data, and communications.

Contribution

A novel convex optimization method for jointly identifying source locations and memberships in superimposed signals with provable near-optimal recovery guarantees.

Findings

Achieves exact recovery under certain conditions

Demonstrates effectiveness through numerical examples

Applicable to various fields like imaging and neural data

Abstract

We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional super-resolution single-molecule imaging, neural spike sorting, multi-user channel identification, among others. We propose a novel algorithm, based on convex programming, and establish its near-optimal performance guarantee for exact recovery by exploiting the sparsity of the point source model as well as incoherence between the point spread functions. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.