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

arXiv: https://arxiv.org/abs/1509.02811 · HTML: https://mlsanity.com/paper/1509.02811/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2015.

## Built on by (most cited first, 1 of 1)

- [A unified consensus-based parallel ADMM algorithm for high-dimensional regression with combined regularizations](https://mlsanity.com/paper/2311.12319/) (2023)

## Abstract (arXiv)

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 ℓ1 norm was used as a sparsity-inducing convex penalty function for the fused lasso signal approximation problem. However, the ℓ1 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.