An Online Parallel and Distributed Algorithm for Recursive Estimation of Sparse Signals

TL;DR

This paper introduces a novel online parallel algorithm for recursive sparse signal estimation that converges faster and is easier to implement than existing sequential methods, suitable for real-time applications.

Contribution

The paper presents a new parallel recursive estimation scheme for sparse signals that improves convergence speed and simplifies implementation compared to prior sequential algorithms.

Findings

Faster convergence than state-of-the-art sequential schemes

Closed-form expressions enable real-time online implementation

Effective in both centralized and distributed settings

Abstract

In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel estimation scheme that consists in solving a sequence of $\ell_{1}$-regularized least-square problems approximately. The proposed scheme is novel in three aspects: i) all elements of the unknown vector variable are updated in parallel at each time instance, and convergence speed is much faster than state-of-the-art schemes which update the elements sequentially; ii) both the update direction and stepsize of each element have simple closed-form expressions, so the algorithm is suitable for online (real-time) implementation; and iii) the stepsize is designed to accelerate the convergence but it does not suffer from the common trouble of parameter tuning in literature. Both centralized and distributed implementation schemes are discussed. The attractive features of the proposed algorithm are also numerically consolidated.