AbstractA new type of robust numeric solution of one form of the Fredholm integral equations of the first king has been discovered. This discovery has its most immediate and important applications in the deconvolution or deblurring of data acquired using scientific instruments. A solution of this integral equation has very general applications. For example, investigator‐controlled mapping of the instrumental point‐spread function to a more useful form is made feasible. The solution of the linear systems imaging model integral equation results from operations performed on the instrumental kernel, response, or point‐spread function with the direct result being the production of a robust, effective inverse kernel. The effective inverse is robust even in the presence of noise. The generation of the inverse kernel in no way depends on the observational data. Therefore, the image enhancement produced by this method contrasts with other numeric schemes that operate only on the observed data. This is an important distinction. This technique, which uses simple numeric operations, offers the possibility of attaining real‐time data enhancements for observational instruments. The concept of taking control of the instrument kernel or point‐spread function forms the basis of the work presented. Investigations of the application of artificial neural networks to resolution enhancement of Hubble Space Telescope imagery have led to a novel extended instrument paradigm that permits reliable and robust resolution enhancement. In addition to resolution enhancement, the fruits of this investigation have provided a powerful data mapping tool that permits nontrivial, numeric apodization of observed data. The applications of the novel convolution connection paradigm neural network has a great potential for multidisciplinary applications such as resolution enhancement of image and spec
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