11 March 2015 Optimal color image restoration: Wiener filter and quaternion Fourier transform
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In this paper, we consider the model of quaternion signal degradation when the signal is convoluted and an additive noise is added. The classical model of such a model leads to the solution of the optimal Wiener filter, where the optimality with respect to the mean square error. The characteristic of this filter can be found in the frequency domain by using the Fourier transform. For quaternion signals, the inverse problem is complicated by the fact that the quaternion arithmetic is not commutative. The quaternion Fourier transform does not map the convolution to the operation of multiplication. In this paper, we analyze the linear model of the signal and image degradation with an additive independent noise and the optimal filtration of the signal and images in the frequency domain and in the quaternion space.
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Artyom M. Grigoryan, Artyom M. Grigoryan, Sos S. Agaian, Sos S. Agaian, "Optimal color image restoration: Wiener filter and quaternion Fourier transform", Proc. SPIE 9411, Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015, 94110P (11 March 2015); doi: 10.1117/12.2083518; https://doi.org/10.1117/12.2083518


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