A new image deblurring approach using a special convolution expansion

The deconvolution problem in image processing consists of reconstructing an original image from an observed and thus a degraded one. This degradation is often modelled as a linear operator plus an additive noise. The linear operator is called the blurring operator and the goal consists of deblurring the image. Very often, the blurring operator is modelled as a convolution whose kernel (the Point Spread Function) is not directly known in practice. In this paper, we first propose a new model for convolution which then validate through computer simulations. Basically, we expend the kernel leading to a sequence of real coefficients connected with the moment problem. We particularly emphasize the radial isotropic case.