Super-Resolution From Binary Measurements With Unknown Threshold

TL;DR

This paper introduces a convex optimization-based algorithm for super-resolution of point sources from binary measurements with unknown thresholds, demonstrating effective recovery of source locations and amplitudes even with noise and blurring.

Contribution

It presents the binary super-resolution (BSR) algorithm that recovers point sources from binary measurements without known thresholds, advancing super-resolution techniques.

Findings

Successful recovery of source locations and amplitudes in simulations

Effective handling of noisy measurements with about 22 dB SNR

Robust performance despite significant blurring

Abstract

We address the problem of super-resolution of point sources from binary measurements, where random projections of the blurred measurement of the actual signal are encoded using only the sign information. The threshold used for binary quantization is not known to the decoder. We develop an algorithm that solves convex programs iteratively and achieves signal recovery. The proposed algorithm, which we refer to as the binary super-resolution (BSR) algorithm, recovers point sources with reasonable accuracy, albeit up to a scale factor. We show through simulations that the BSR algorithm is successful in recovering the locations and the amplitudes of the point sources, even in the presence of significant amount of blurring. We also propose a framework for handling noisy measurements and demonstrate that BSR gives a reliable reconstruction (correspondingly, reconstruction signal-to-noise ratio (SNR) of about 22 dB) for a measurement SNR of 15 dB.