Deblurring Gaussian Blur (Classic Reprint)

Excerpt from Deblurring Gaussian Blur O'a' stably among original functions f(x) that are well approximated by polynomials of fixed degree. These kernels will provide exact reconstructions of (sufficiently low order) polynomial original data. The existence and use of these kernels has been presented elsewhere [john]; our analysis is new only in that we emphasize the use of Hermite polynomials, and give explicit formulas in terms of Hermite polynomials. The problem of reconstructing f(x) given h(x) and t is the inverse heat ... Read More

Excerpt from Deblurring Gaussian Blur O'a' stably among original functions f(x) that are well approximated by polynomials of fixed degree. These kernels will provide exact reconstructions of (sufficiently low order) polynomial original data. The existence and use of these kernels has been presented elsewhere [john]; our analysis is new only in that we emphasize the use of Hermite polynomials, and give explicit formulas in terms of Hermite polynomials. The problem of reconstructing f(x) given h(x) and t is the inverse heat equation problem, since the function h(x) represents a distribution of heat after t units of time, where f(x) is the initial t 0 distribution. Solving the heat equation backwards in time is an interesting inverse problem with applications in image enhancement, signal and image representation, and perhaps even modeling of neural processes for analyzing data. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. Read Less