Rolling-circles: Detect and reduce noise via erosion of
finite-difference moduli for preserving signals
DIGITAL SIGNAL PROCESSING, (2020)DOI: 10.1016/j.dsp.2020.102764
Abstract
Noise is ubiquitous in nature; it decreases the measurement or data
reliability. This reliability may be increased by using a novel method
that detects and reduces noise for preserving signals, called the
Rolling-circle method. Our method treats noisy signals by eroding
finite-difference moduli, circle radii, with either a version for
denoising signals or a version for smoothing signals. Both versions were
compared to a moving average filter, a simple median filter, an adaptive
median filter, a Savitzky-Golay filter, and two wavelet threshold
filters. For these filters, we tested four cases: denoising a histogram,
denoising a Raman spectrum, smoothing a well-log, and denoising a
synthetic signal. In such cases, our method has surpassed the mentioned
filters as measured through well-known metrics. A quantitative metric,
called 0-metric, is also proposed in this work for assessing the amount
of preserved data. The preservation of a clean signal was only achieved
entirely by the proposed method, which we believe that no filter ever
did thus far. (C) 2020 Elsevier Inc. All rights reserved.