k-dimensional error-free deconvolution using the fermat number transform

✍ Scribed by M. Morháč

• Book ID: 103930531
• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 602 KB
• Volume: 18
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(89)90030-8

✦ Synopsis

The paper presents the generalization of the one-dimensional deconvolution algorithm using the Fermat number transform for the k-dimensional deconvolution. The problems of how to express a k-dimensional convolution system in the form of special matrix equation, how to calculate the precise value of the matrix determinant and how to remove rounding-off errors in the process of deconvolution, are solved in the paper. The results are used in the algorithm derivation.

where the matrix hk has the dimension Nk x Nk. From the above we can see 'hat the k-dimensional convolution can be written as a special system of linear equations.