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

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