# Generalized Multi-Order Total Variation for Signal Restoration

## TL;DR

This paper introduces GMO-TV, a novel multi-order total variation regularization method that improves signal restoration by modeling inter-relationships between derivatives and automatically tuning parameters, outperforming existing methods.

## Contribution

It proposes GMO-TV with a multivariate Laplacian prior and an automatic parameter selection framework, advancing regularization techniques for signal restoration.

## Key findings

- GMO-TV outperforms related regularization methods on ECG and EEG signals.
- The method effectively models relationships between multiple derivative orders.
- Automatic parameter determination enhances usability and performance.

## Abstract

Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV promotes piece-wise linear reconstructions. Generalized Multi-Order Total Variation (GMO-TV) is proposed as a novel regularization method which incorporates a new multivariate Laplacian prior on signal derivatives in a non-quadratic regularization functional, that utilizes subtle inter-relationship between multiple order derivatives. We also propose a computational framework to automatically determine the weight parameters associated with these derivative orders, rather than treating them as user parameters. Using simulation results on ECG and EEG signals, we show that GMO-TV performs better than related regularization functionals.