Level Set Estimation from Compressive Measurements using Box Constrained Total Variation Regularization

TL;DR

This paper introduces a method for estimating signal level sets from incomplete, noisy measurements using box-constrained Total Variation regularization, applicable in fields like medical imaging and astronomy.

Contribution

It proposes a novel approach leveraging box-constrained TV regularization for level set estimation from compressive, noisy measurements, demonstrating improved performance over existing methods.

Findings

Effective in reconstructing level sets from highly incomplete data

Robust to additive noise in measurements

Outperforms state-of-the-art techniques in simulations

Abstract

Estimating the level set of a signal from measurements is a task that arises in a variety of fields, including medical imaging, astronomy, and digital elevation mapping. Motivated by scenarios where accurate and complete measurements of the signal may not available, we examine here a simple procedure for estimating the level set of a signal from highly incomplete measurements, which may additionally be corrupted by additive noise. The proposed procedure is based on box-constrained Total Variation (TV) regularization. We demonstrate the performance of our approach, relative to existing state-of-the-art techniques for level set estimation from compressive measurements, via several simulation examples.