Abstract
This article analytically studies the dependence of components of the error of reconstructing the true signal on the number of rows of a random projection matrix. It is shown that, with increasing the dimension of the random projector, the deterministic error component decreases and the stochastic one increases. Expressions are obtained for calculating the interval of noise levels that ensure the availability of the global minimum of the error. The analytical results are confirmed by numerical experiments.
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2015, pp. 160–173.
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Revunova, E.G. Analytical Study of Error Components for Solving Discrete Ill-Posed Problems Using Random Projections. Cybern Syst Anal 51, 978–991 (2015). https://doi.org/10.1007/s10559-015-9791-0
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DOI: https://doi.org/10.1007/s10559-015-9791-0