A new method for D-dimensional exact deconvolution

Date

1999-05-01

Author

Tuncer, Temel Engin

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Deconvolution is an important problem of signal processing, and conventional approaches. including Fourier methods, have stability problems due to the zeros of the convolution kernel. In this paper, we present a new method of multidimensional exact deconvolution. This method is always stable, even when the convolution kernel h(n) has zeros on the unit circle, and there exist closed-form solutions for the one-dimensional (1-D) case (D = 1). For the multidimensional case (D > 1), the proposed method yields stable solutions when dete(h) = 0. This solution set covers a portion of all possible convolution kernels, including the ones that have zeros on the multidimensional unit circle, This novel time-domain method is based on the fact that the convolution inverse of a first-order kernel can be found exactly in multidimensional space. Convolution inverses for higher order kernels are obtained using this fact and the zeros of the convolution kernel, The presented method is enact, stable, and computationally efficient, Several examples are given in order to show the performance of this method in 1-D and multidimensional cases.

Subject Keywords

Deconvolution, System identification, Signal restoration, Multidimensional filtering, Inverse filtering

URI

https://hdl.handle.net/11511/44482

Journal

IEEE TRANSACTIONS ON SIGNAL PROCESSING

DOI

https://doi.org/10.1109/78.757220

Collections

Department of Electrical and Electronics Engineering, Article

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Citation Formats

T. E. Tuncer, “A new method for D-dimensional exact deconvolution,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, pp. 1324–1334, 1999, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44482.