Deblurring Gaussian blur
Bart M. ter Haar Romeny, Luc M. J. Florack, M. Swart, Janita Wilting, Max A. Viergever · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
To enhance Gaussian blurred images the structure of Gaussian scale-space is studied in a small environment along the scale axis. A local Taylor-expansion in the negative scale-direction requires the calculation of high order derivatives with respect to scale. The generating differential equation for linear scale- space, the isotropic diffusion equation, relates these derivatives to spatial Laplaceans. The high order spatial derivatives are calculated by means of convolution with Gaussian derivative kernels, enabling well-posed differentiation. Deblurring incorporating even 32th order spatial derivatives is accomplished successfully. A physical limit is experimentally shown for the Gaussian derivatives due to discrete raster representation and coarseness of the intensity discretization.