Super-resolution via superset selection and pruning

TL;DR

The paper introduces the superset method, a pursuit-like algorithm for super-resolution sparse vector recovery from Fourier measurements, which outperforms existing methods in noiseless scenarios and extends to higher dimensions.

Contribution

The paper proposes the superset method, a novel pursuit-like algorithm that guarantees success in noiseless super-resolution and generalizes to higher dimensions.

Findings

Always successful in noiseless recovery

Demonstrates robustness to noise numerically

Extends applicability to higher-dimensional problems

Abstract

We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the translation invariance of the Fourier transform, followed by a removal step to estimate the solution's support. The superset method is always successful in the noiseless regime (unlike L1-minimization) and generalizes to higher dimensions (unlike the matrix pencil method). Relative robustness to noise is demonstrated numerically.