Block Iterative Reweighted Algorithms for Super-Resolution of Spectrally Sparse Signals

TL;DR

This paper introduces new block iterative reweighted algorithms that significantly improve the accuracy and speed of super-resolving spectrally sparse signals with unknown frequencies from limited data.

Contribution

The paper presents novel algorithms that leverage support knowledge iteratively to enhance frequency recovery beyond existing atomic norm minimization methods.

Findings

Better recovery performance than existing methods

Faster computational speed

Effective in super-resolution of spectrally sparse signals

Abstract

We propose novel algorithms that enhance the performance of recovering unknown continuous-valued frequencies from undersampled signals. Our iterative reweighted frequency recovery algorithms employ the support knowledge gained from earlier steps of our algorithms as block prior information to enhance frequency recovery. Our methods improve the performance of the atomic norm minimization which is a useful heuristic in recovering continuous-valued frequency contents. Numerical results demonstrate that our block iterative reweighted methods provide both better recovery performance and faster speed than other known methods.