A Fast and Robust Reconstruction of Finite Rate of Innovation Signal via a Non-Iterative Method

Recently, sparse sampling and reconstruction is an important topic, and many methods have been proposed to handle it. The finite rate of innovation (FRI) theory provides a good solution for the sparse problem and has been applied to broad scenarios due to its excellent performance. However, most FRI reconstruction algorithms work in an iterative manner to reduce the effect of noise, which does not satisfy the requirements for real-time applications. In this paper, we develop the algorithm to retrieve the FRI signal with low computation cost via a non-iterative method. The proposed method has a similar performance to classical Cadzow's iterative algorithm but with a lower computation cost. The validity of our method is demonstrated both in simulations and real acoustic data in underwater.