Computational time-reversal imaging with a small number of random and noisy measurements

TL;DR

This paper explores a novel approach to computational time reversal imaging that effectively locates multiple scatterers using limited, noisy measurements by approximating the null subspace through randomized methods.

Contribution

It introduces a new randomized approximation technique for the null subspace, enabling imaging with fewer and noisier measurements than traditional methods.

Findings

Effective localization of scatterers with fewer measurements

Robustness to measurement noise demonstrated

Approximation of null subspace via randomized methods

Abstract

Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator, obtained through the singular value decomposition of the frequency response matrix. Here, we discuss the image recovery problem from a small number of random and noisy measurements, and we show that this problem is equivalent to a randomized approximation of the null subspace of the frequency response matrix.