A theory of digital picture restoration by using the generalized laplacian—successive elimination method

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Abstract
A digital image is represented by elements of a vector space whose dimensionality equals the number of pixels and linear spatial degradation of a picture is regarded as a linear operator on the vector space. In existing picture restoration theories, especially the theory using a numerical analysis method, this operator is represented by a matrix and the restoration problem is treated as that of obtaining the generalized inverse. In this restoration theory, as the number of pixels increases, the dimensionality of the matrix becomes so large that it becomes very difficult to compute the inverse matrix. In this paper, the generalized Laplacian which is constructed from the linear operator representing degradation is introduced and, by using this operator, the original picture can be restored with high accuracy, simple operations and short computation time. This theory is very effective if the degradation operation is shift‐invariant.

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