Compressed sensing with a jackknife and a bootstrap

TL;DR

This paper introduces a method using jackknife and bootstrap techniques to estimate and visualize errors in compressed sensing reconstructions, providing confidence regions without needing full ground truth data.

Contribution

The study demonstrates that statistical error estimation tools can produce reliable error visualizations in compressed sensing, enhancing confidence in reconstructed images.

Findings

Error 'bars' accurately reflect true errors in reconstructed images

Error visualizations reveal structure of potential artifacts

Method validated on datasets with known ground truth

Abstract

Compressed sensing proposes to reconstruct more degrees of freedom in a signal than the number of values actually measured. Compressed sensing therefore risks introducing errors -- inserting spurious artifacts or masking the abnormalities that medical imaging seeks to discover. The present case study of estimating errors using the standard statistical tools of a jackknife and a bootstrap yields error "bars" in the form of full images that are remarkably representative of the actual errors (at least when evaluated and validated on data sets for which the ground truth and hence the actual error is available). These images show the structure of possible errors -- without recourse to measuring the entire ground truth directly -- and build confidence in regions of the images where the estimated errors are small.