Practical error estimates for sparse recovery in linear inverse problems

TL;DR

This paper evaluates the practical accuracy of sparse recovery methods in linear inverse problems, analyzing how factors like sparsity, data quantity, noise, and measurement properties affect reconstruction quality, with real-world magnetic tomography examples.

Contribution

It provides empirical error estimates for sparse recovery in realistic scenarios, bridging the gap between theory and practice in linear inverse problems.

Findings

Reconstruction errors depend on sparsity, data, noise, and measurement matrix properties.

Empirical errors are compared with theoretical bounds.

Magnetic tomography example illustrates practical applicability.

Abstract

The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors (depending on the sparsity of the desired solution, the number of data, the noise level on the data, and various properties of the measurement matrix); they are compared to known theoretical bounds and illustrated on a magnetic tomography example.