A Kalman Filter Framework for Simultaneous LTI Filtering and Total Variation Denoising

Abstract

This paper proposes a Kalman filter framework for signal denoising that simultaneously utilizes conventional linear time-invariant (LTI) filtering and total variation (TV) denoising. In this approach, the desired signal is considered to be a mixture of two distinct components: a band-limited (e.g., low-frequency component, high-frequency component) signal and a sparse-derivative signal. An iterative Kalman filter/smoother approach is formulated where zero-phase LTI filtering is used to estimate the band-limited signal and TV denoising is used to estimate the sparse-derivative signal.