Optimal restoration of multiple signals in quaternion algebra

Artyom M. Grigoryan; Sos S. Agaian

doi:10.1117/12.2558209

21 April 2020 Optimal restoration of multiple signals in quaternion algebra

Artyom M. Grigoryan, Sos S. Agaian

Proceedings Volume 11399, Mobile Multimedia/Image Processing, Security, and Applications 2020; 1139909 (2020) https://doi.org/10.1117/12.2558209
Event: SPIE Defense + Commercial Sensing, 2020, Online Only

Abstract

This paper offers a new multiple signal restoration tool to solve the inverse problem, when signals are convoluted with a multiple impulse response and then degraded by an additive noise signal with multiple components. Inverse problems arise practically in all areas of science and engineering and refers to as methods of estimating data/parameters, in our case of multiple signals that cannot directly be observed. The presented tool is based on the mapping multiple signals into the quaternion domain, and then solving the inverse problem. Due to the non-commutativity of quaternion arithmetic, it is difficult to find the optimal filter in the frequency domain for degraded quaternion signals. As an alternative, we introduce an optimal filter by using special 4×4 matrices on the discrete Fourier transforms of signal components, at each frequency point. The optimality of the solution is with respect to the mean-square-root error, as in the classical theory of the signal restoration by the Wiener filter. The Illustrative example of optimal filtration of multiple degraded signals in the quaternion domain is given. The computer simulations validate the effectiveness of the proposed method.

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Citation Download Citation

Artyom M. Grigoryan and Sos S. Agaian "Optimal restoration of multiple signals in quaternion algebra", Proc. SPIE 11399, Mobile Multimedia/Image Processing, Security, and Applications 2020, 1139909 (21 April 2020); https://doi.org/10.1117/12.2558209

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