Learning to Sample: Data-Driven Sampling and Reconstruction of FRI Signals

TL;DR

This paper introduces a joint optimization framework combining greedy sampling and learning-based sparse recovery for FRI signals, enabling improved reconstruction at sub-Nyquist rates without requiring exact pulse knowledge.

Contribution

It proposes a novel data-driven method that jointly optimizes sampling and reconstruction, handling variable sampling rates and improving accuracy over existing methods.

Findings

Lower reconstruction error with the proposed joint design.

Effective in both noisy and clean scenarios.

Applicable to various sampling setups including compressed sensing.

Abstract

Finite-rate-of-innovation (FRI) signals are ubiquitous in applications such as radar, ultrasound, and time of flight imaging. Due to their finite degrees of freedom, FRI signals can be sampled at sub-Nyquist rates using appropriate sampling kernels and reconstructed using sparse-recovery algorithms. Typically, Fourier samples of the FRI signals are used for reconstruction. The reconstruction quality depends on the choice of Fourier samples and recovery method. In this paper, we consider to jointly optimize the choice of Fourier samples and reconstruction parameters. Our framework is a combination of a greedy subsampling algorithm and a learning-based sparse recovery method. Unlike existing techniques, the proposed algorithm can flexibly handle changes in the sampling rate and does not suffer from differentiability issues during training. Importantly, exact knowledge of the FRI pulse is not required. Numerical results show that, for a given number of samples, the proposed joint design leads to lower reconstruction error for FRI signals compared to independent data-driven design methods for both noisy and clean samples. Our learning to sample approach can be readily applied to other sampling setups as well including compressed sensing problems.