Accelerating cross-validation with total variation and its application to super-resolution imaging

TL;DR

This paper introduces an approximation formula to efficiently estimate cross-validation error in sparse linear regression with total variation, significantly reducing computational costs and demonstrated on super-resolution black-hole imaging.

Contribution

The paper presents a novel approximation method for cross-validation error that leverages perturbative expansion, applicable to high-dimensional data and models, enhancing computational efficiency.

Findings

Approximation formula accurately estimates CVE with high precision.

Method reduces computational cost of cross-validation significantly.

Application to black-hole image reconstruction demonstrates practical effectiveness.

Abstract

We develop an approximation formula for the cross-validation error (CVE) of a sparse linear regression penalized by $\ell_1$-norm and total variation terms, which is based on a perturbative expansion utilizing the largeness of both the data dimensionality and the model. The developed formula allows us to reduce the necessary computational cost of the CVE evaluation significantly. The practicality of the formula is tested through application to simulated black-hole image reconstruction on the event-horizon scale with super resolution. The results demonstrate that our approximation reproduces the CVE values obtained via literally conducted cross-validation with reasonably good precision.