Exact Sparse Approximation Problems via Mixed-Integer Programming: Formulations and Computational Performance
This paper deals with the estimation of the arrival times of overlapping ultrasonic echoes. We focus on approaches based on discrete sparse deconvolution. Such methods are limited by the time resolution imposed by the model discretization, which is usually considered at the data sampling rate. In order to get closer to the continuous-time model, we propose to increase the time precision by introducing an up-sampling factor in the discrete model. The problem is then recast as a Multiple Input Single Output (MISO) deconvolution problem. Then, we propose to revisit standard sparse deconvolution algorithms for MISO systems. Specific and efficient algorithmic implementation is derived in such setting. Algorithms are evaluated on synthetic data, showing improvements in robustness toward discretization errors and competitive computational time compared to the standard approaches.