Sparse reconstruction based on iterative TF domain filtering and Viterbi based IF estimation algorithm

Abstract This paper presents a solution to the problem of reconstructing sparsely sampled signals using time-frequency (TF) filtering. The proposed method employs a modified Viterbi algorithm and adaptive directional TF distributions (ADTFD) for the accurate estimation of the instantaneous frequency (IF) estimation of sparsely sampled multi-component signals from a given signal. Using the IF information, TF filtering is performed to separate the signal components. This TF filtering operation also fills the gaps caused by missing samples. The separated components are then added up, and known values are re-inserted to obtain a reconstructed signal. The steps above involving IF estimation, TF filtering, and re-insertion of known values are again applied with the reconstructed signal as an input signal. This algorithm is iterated until the difference between the signal energy in two successive iterations falls below a certain threshold. Experimental results indicate the superiority of the proposed method. The code for reproducing the results can be accessed from https://github.com/mokhtarmohammadi/Sparse-Reconstruction .