Exponential-Reproducing-Kernel-Based Sparse Sampling Method for Finite Rate of Innovation Signal with Arbitrary Pulse Echo Position

Abstract

An exponential reproducing kernel (ERK) has been applied to data sparse sampling for finite rate of innovation (FRI) signals with the characteristic of flexible parameter setting in contrast to other sampling kernels. However, the signal reconstruction process may fail if a pulse echo is present in certain positions. To solve this problem, a novel ERK sparse sampling method was developed for arbitrary pulse echo positions. A constraint relationship between the pulse echo position and reproduced-exponent area was deduced, revealing the cause of invalid signal reconstruction from sparse sampling data. A new sampling time interval calculation algorithm is presented in this paper. Through the proposed method, FRI signals can be reconstructed accurately with a pulse echo present at arbitrary positions without increasing the quantity of sparse sampling data. The signal reconstruction effectiveness and accuracy were verified through simulation experiments. The proposed technique can be used to improve the flexibility of the ERK sparse sampling method in actual applications.