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The Effects of Noise on the Missing‐Data‐Residue Technique
Author(s) -
Doherty G. K.,
Poland G. A.
Publication year - 1996
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889896000167
Subject(s) - smoothing , missing data , noise (video) , data point , residue (chemistry) , statistics , observational error , mathematics , algorithm , computer science , chemistry , artificial intelligence , biochemistry , image (mathematics)
The missing‐data‐residue technique is a method of recovering the scatter intensity curve at low‐ Q values from small‐angle scattering data. The effect on the missing‐data‐residue technique of the addition of varying degrees of noise to truncated analytical particles is investigated, with the noise levels varying from 0 to ±10%. The effects of smoothing of the data prior to the application of the technique are also investigated. The results for nonsmoothed data are shown to degrade in proportion to the noise level and it is shown that an estimate of the noise level gives an estimate of the potential error on the result. The five‐point moving‐average smoothing used is shown to improve the variance of the returned zero‐angle scatter intensity but at the expense of potentially introducing a small error. Results for both smoothed and nonsmoothed data are compared and it is shown that smoothing of the data is preferable, even at relatively low noise levels. For both smoothed and nonsmoothed data, a correlation is shown to exist between the error on the first known I ( Q ) data point and the returned I (0).