Spatial-domain Convolution/deconvolution Transform
نویسنده
چکیده
A new linear transform is deened for real valued functions which can be expanded in Taylor series. For an image which can be expressed by the Taylor expansion of a function, the new transform corresponds to convolution of the image with a point spread function. The point spread function must satisfy the condition that it's zero-th moment is non-zero and positive integer moments are nite. The forward part of the new transform is based on a spatial-domain convolution formula rst derived by Pa-poulis in 1962. The inverse of the new transform corresponds to deconvolution. This transform suggests a direct spatial-domain approach to convolution and deconvolu-tion operations on images. In practice, the transform can be implemented by local operations on images using global characteristics of point spread functions speciied by their rst few moments. Therefore, this transform is better suited than the Fourier transform for many image ltering operations such as restoration of defocused images and image enhancement. The new transform is rst derived for one-dimensional signals. It is then extended to two-dimensional images and multi-dimensional signals. A modiied version of the transform is deened for discrete signals.
منابع مشابه
Application of Spatial-Domain Convolution/Deconvolution Transform for Determining Distance from Image Defocus
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