Revisit 1D Total Variation restoration problem with new real-time algorithms for signal and hyper-parameter estimations

TL;DR

This paper introduces a real-time 1D Total Variation denoising algorithm with an automatic hyper-parameter selection method, enabling fast and effective signal restoration suitable for real-time applications.

Contribution

It presents a new heuristic for automatic lambda selection and develops both offline and online algorithms with improved computational efficiency for 1D TV denoising.

Findings

The online algorithm runs in O(n) time.

The automatic lambda selection performs comparably to state-of-the-art methods.

The proposed methods enable real-time signal denoising applications.

Abstract

1D Total Variation (TV) denoising, considering the data fidelity and the Total Variation (TV) regularization, proposes a good restored signal preserving shape edges. The main issue is how to choose the weight $\lambda$ balancing those two terms. In practice, this parameter is selected by assessing a list of candidates (e.g. cross validation), which is inappropriate for the real time application. In this work, we revisit 1D Total Variation restoration algorithm proposed by Tibshirani and Taylor. A heuristic method is integrated for estimating a good choice of $\lambda$ based on the extremums number of restored signal. We propose an offline version of restoration algorithm in O(n log n) as well as its online implementation in O(n). Combining the rapid algorithm and the automatic choice of $\lambda$, we propose a real-time automatic denoising algorithm, providing a large application fields. The simulations show that our proposition of $\lambda$ has a similar performance as the states of the art.