Sparse time–frequency distributions based on the $$\ell _1$$ ℓ 1 -norm minimization with the fast intersection of confidence intervals rule

Abstract

Methods based on the sparsity constraint have been recently introduced to the time–frequency (TF) signal processing, achieving artifact suppression by exploiting the fact that most real-life signals are sparse in the TF domain. In this paper, we propose a sparse reconstruction algorithm based on the two-step iterative shrinkage/thresholding (TwIST) algorithm. In the proposed TwIST algorithm modification, the soft-thresholding value is adaptively determined by the fast intersection of the confidence intervals (FICI) rule in each iteration of the reconstruction algorithm. The FICI rule is used to determine the TF region with the lowest mean value, and the soft-thresholding value is set to the largest sample value inside the region. The performance of the proposed algorithm has been compared to the performance of the state-of-the-art reconstruction algorithms in terms of their execution time and concentration of the resulting TF distribution.