Informatics and Applications
2022, Volume 16, Issue 2, pp 44-51
THE USE OF THE FDR METHOD OF MULTIPLE HYPOTHESIS TESTING WHEN INVERTING LINEAR HOMOGENEOUS OPERATORS
- S. I. Palionnaya
- O. V. Shestakov
Abstract
One of the important tasks when processing large data arrays is their economical representation. To solve this task, it is necessary to identify significant features and remove noise. Such problems are found in a wide variety of fields such as genetics, biology, astronomy, computer graphics, audio and video data processing, etc. Modern research in this area describes various filtering methods based on a sparse representation of the obtained experimental data. To construct statistical estimates based on the observed data, the procedure of multiple testing of hypotheses about the significance of observations is widely used. The present authors consider the FDR (false discovery rate) method based on the control of the expected proportion of false rejections of the null hypothesis and the Benjamin-Hochberg algorithm for multiple hypothesis testing. Often, the information available for observation is some kind of transformation of the data of interest. This additionally raises the problem of inverting this transformation. The present authors consider the case when the original data vector is subjected to some linear homogeneous transformation. Such situations are typical, for example, in astrophysical and tomographic applications.
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[+] About this article
Title
THE USE OF THE FDR METHOD OF MULTIPLE HYPOTHESIS TESTING WHEN INVERTING LINEAR HOMOGENEOUS OPERATORS
Journal
Informatics and Applications
2022, Volume 16, Issue 2, pp 44-51
Cover Date
2022-07-25
DOI
10.14357/19922264220206
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; thresholding; multiple hypothesis testing; linear homogeneous operator; unbiased risk estimate
Authors
S. I. Palionnaya  ,  and O. V. Shestakov , , 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University,
1 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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