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In this chapter, we consider the model of quaternion signal (or image) degradation when the signal (or image) 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 and images, 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 chapter, we analyze the linear model of the signal and image degradation with an additive independent noise and describe the simple optimal filtration of the quaternion signals and images in the frequency domain.
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