Benchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization

TL;DR

This paper compares three advanced signal processing methods—filter diagonalization, compressed sensing, and super-resolution—to determine their effectiveness across various signal types, providing guidance on their optimal applications.

Contribution

The study systematically benchmarks these methods on diverse signals, highlighting their strengths and limitations for practical scientific and engineering applications.

Findings

Filter diagonalization excels with Lorentzian signals.

Compressed sensing and super-resolution are better for arbitrary signals.

Guidelines for choosing the appropriate method based on signal type.

Abstract

Signal processing techniques have been developed that use different strategies to bypass the Nyquist sampling theorem in order to recover more information than a traditional discrete Fourier transform. Here we examine three such methods: filter diagonalization, compressed sensing, and super-resolution. We apply them to a broad range of signal forms commonly found in science and engineering in order to discover when and how each method can be used most profitably. We find that filter diagonalization provides the best results for Lorentzian signals, while compressed sensing and super-resolution perform better for arbitrary signals.