Analytical study of error components for solving discrete ill-posed problems using random projections
EG Revunova - Cybernetics and Systems Analysis, 2015 - Springer
Cybernetics and Systems Analysis, 2015•Springer
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.
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.
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.
Springer
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