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

Finite-rate-of-innovation (FRI) signal model is well suited for time-of-flight imaging applications such as ultrasound, lidar, sonar, radar, and more. Due to their finite degrees of freedom, the sub-Nyquist sampling framework used FRI signals. In this framework, achieved by using appropriate kernels. Reconstruction performed first computing Fourier samples then applying sparse-recovery algorithms. The choice reconstruction method plays a crucial role in quality. paper, we consider jointly optimizing parameters. Our combines greedy subsampling algorithm learning-based sparse recovery method. combination has three distinct advantages. First, network does not require knowledge pulse shape, which case with existing approaches. Second, suffer from differentiability issues during training common networks. Further, proposed can flexibly handle changes rate. Numerical results show that, given number samples, joint design leads lower error signals than independent data-driven methods noisy clean samples. We also propose way extend approach large-scale problems. learning-to-sample be readily applied other setups, including compressed sensing