Abstract
Discrete convolution is a very important operation for filter design, image restoration, and applications [4,8, 10,11,16].In this paper, we investigate the existence of inverse elements in respect to convolution, and we derive a method to compute inverse elements without using Fourier transform. Furthermore, we get a simple condition for existence of inverse elements which is easy to verify. We describe the computation of small convolution kernels. These small convolution kernels are least squares optimal [15]. By a simple idea, we can regularize the problem, and the computational effort can be reduced drastically. Furthermore, we can use this theory to restore noise pictures, and we can develop a regularization theory. For the clarity of presentation, the approach given here is one-dimensional, but the multidimensional generalization is straightforward.
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© 1993 Springer-Verlag Berlin Heidelberg
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Suesse, H., Voss, K. (1993). Inversion of convolution by small kernels. In: Chetverikov, D., Kropatsch, W.G. (eds) Computer Analysis of Images and Patterns. CAIP 1993. Lecture Notes in Computer Science, vol 719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57233-3_16
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DOI: https://doi.org/10.1007/3-540-57233-3_16
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