A fast local PPF restoration filter

A local spatial convolution filter is suggested whose design is based on approximating a global optimal restoration filter, the Parametric Projection Filter (PPF). The PPF tries to construct a restored signal or image that is optimally close to each individual original signal, with the noise level as low as possible. The local filter provides a restoration that is as close as possible to the PPF restoration. The design is accomplished by least squares techique in Fourier domain. Once the PPF is available, the main task is to solve a set of linear normal equations whose coefficient size depends on the size of the local filter. It is shown by examples using both one- and two-dimensional signals that the restorations are satisfactory even when the filter size is considerably smaller than the width of the degradation.