GCD-based Blind Deconvolution using PCA-based Noise Reduction

A. Tanaka, K. Azuma, and M. Miyakoshi (Japan)


blind deconvolution, GCD, PCA, noise reduction, perturbation


Blind deconvolution is a technique of restoring an unknown original signal only from its convolutive observations. A greatest-common-divisor(GCD)-based method is recognized as one of popular blind deconvolution algorithms. However in general, the solution by this method may be unstable due to the existence of observation noises. A method aiming to improve the stability have been proposed. However, the performance and the mathematical analyses of the method are still insufficient. In this paper, we analyse the perturbation of an estimated solution by the existence of the noise and propose a robust GCD-based blind deconvolution method. The basic idea of the proposed method is based on obtaining the GCD of two linear combinations of more than two observations. The coefficients used to obtain the linear combinations are chosen by PCA of all observations. Moreover, we discuss the theoretical validity of using the proposed linear combinations to obtain the solution. The results of numerical examples are also shown to verify the efficacy of the proposed method.

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