Sparsity-assisted signal smoothing (revisited)

Abstract

This paper proposes an improved formulation of sparsity-assisted signal smoothing (SASS). The purpose of SASS is to filter/denoise a signal that has jump discontinuities in its derivative (of some designated order) but is otherwise smooth. SASS unifies conventional low-pass filtering and total variation denoising. The SASS algorithm depends on the formulation, in terms of banded Toeplitz matrices, of a zero-phase recursive discrete-time filter as applied to finite-length data. The improved formulation presented in this paper avoids the unwanted end-point transient artifacts which sometimes occur in the original version. For illustration, SASS is applied to ECG signal denoising.