An enhanced weighted greedy analysis pursuit algorithm with application to EEG signal reconstruction

Abstract

In the past decade, compressed sensing (CS) has provided an efficient framework for signal compression and recovery as the intermediate steps in signal processing. The well‐known greedy analysis algorithm, called Greedy Analysis Pursuit (GAP) has the capability of recovering the signals from a restricted number of measurements. In this article, we propose an extension to the GAP to solve the weighted optimization problem satisfying an inequality constraint based on the Lorentzian cost function to modify the EEG signal reconstruction in the presence of heavy‐tailed impulsive noise. Numerical results illustrate the effectiveness of our proposed algorithm, called enhanced weighted GAP (ewGAP) to reinforce the efficiency of the signal reconstruction and provide an appropriate candidate for compressed sensing of the EEG signals. The suggested algorithm achieves promising reconstruction performance and robustness that outperforms other analysis‐based approaches such as GAP, Analysis Subspace Pursuit (ASP), and Analysis Compressive Sampling Matching Pursuit (ACoSaMP).

Sparse Analysis Recovery via Iterative Cosupport Detection Estimation

“…ICDE-L1 performed significantly better than ICDE-L2. Since ABP is not the only algorithm for cosparse signal recovery, another line of future investigation is to apply ICDE to other reconstruction algorithms such as the smoothing-based accelerated alternating minimization [31], reweighted approaches [23], [32], matching pursuit generalized LASSO [33], sophisticated cosparsity inducing function [24], [44], [45], and many others. This article has been accepted for publication in a future issue of this journal, but has not been fully edited.…”

“…A modified GAP algorithm was developed to solve the weighted regularized L2-minimization problem, as proposed in Reference [23]. Mohagheghian et al [24] proposed an enhanced weighted GAP (ewGAP), an extension to the GAP algorithm based on synthesis counterpart Lorentzian norm [25]. Cosparsity-based stagewise matching pursuit (CSMP) [26] employed more sophisticated backtracking methods as an analysis counterpart corresponding to stagewise orthogonal matching pursuit (StOMP) [27].…”

Modified Block Compressed Sensing for Extraction of Fetal Electrocardiogram from Mother Electrocardiogram Using Block Compressed Sensing Based Guided FOCUSS and FAST-Independent Component

“…These methods divide the function into smaller subfunctions, which can be solved separately with efficiency and less computational cost. However, these algorithms suffer during reconstruction from blocking artifacts that are introduced during the regrouping of these subproblems [14]. It can cause loss in vital information.…”