Convex Fused Lasso Denoising with Non-Convex Regularization and its use for Pulse Detection

TL;DR

This paper introduces a convex fused lasso denoising method using non-convex penalties, improving signal estimation accuracy and enabling efficient pulse detection from noisy data.

Contribution

It presents a convex formulation with non-convex penalties for fused lasso, along with an efficient algorithm and application to pulse detection.

Findings

Convexity is maintained with non-convex penalties.

The method improves signal value estimation.

Effective pulse detection demonstrated.

Abstract

We propose a convex formulation of the fused lasso signal approximation problem consisting of non-convex penalty functions. The fused lasso signal model aims to estimate a sparse piecewise constant signal from a noisy observation. Originally, the $\ell_1$ norm was used as a sparsity-inducing convex penalty function for the fused lasso signal approximation problem. However, the $\ell_1$ norm underestimates signal values. Non-convex sparsity-inducing penalty functions better estimate signal values. In this paper, we show how to ensure the convexity of the fused lasso signal approximation problem with non-convex penalty functions. We further derive a computationally efficient algorithm using the majorization-minimization technique. We apply the proposed fused lasso method for the detection of pulses.