Sign data derivative recovery
type: Item
instance of: scholarly article
title: Sign data derivative recovery
zbMATH Open document ID: 1264.94047
DOI: 10.5402/2012/630702
author: Louis M. Houston
author: G. A. Glass
author: A. D. Dymnikov
published in: ISRN Applied Mathematics
publication date: 2013-06-11T00:00:00Z
review text: Summary: Given only the signs of signal plus noise added repetitively or sign data, signal amplitudes can be recovered with minimal variance. However, discrete derivatives of the signal are recovered from sign data with a variance which approaches infinity with decreasing step size and increasing order. For industries such as the seismic industry, which exploits amplitude recovery from sign data, these results place constraints on processing, which includes differentiation of the data. While methods for smoothing noisy data for finite difference calculations are known, sign data requires noisy data. In this paper, we derive the expectation values of continuous and discrete sign data derivatives and we explicitly characterize the variance of discrete sign data derivatives.
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 6172973
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/630702
OpenAlex ID: W2019033777
Wikidata QID: Q58691582
cites work: Q4000373
cites work: Q5508799
description: scientific article; zbMATH DE number 6172973