LEARNING TO SAMPLE FOR SPARSE SIGNALS

Finite-rate-of-innovation (FRI) signals are ubiquitous in radar, ultrasound, and time of flight imaging applications. In this paper, we propose a model-based deep learning approach to jointly design the subsampling and reconstruction of FRI signals. Specifically, our framework is a combination of a greedy subsampling algorithm and a learning-based sparse recovery method. Unlike existing learning-based techniques, the proposed algorithm can flexibly handle changes in the sampling rate and does not suffer from differentiability issues during training. Moreover, exact knowledge of the FRI pulse is not required. Numerical results show that the proposed joint design leads to lower reconstruction error for FRI signals compared with existing benchmark methods for a given number of samples. The method can easily adapt to other sparse recovery problems.