Space/spatial-frequency analysis based filtering

Space-invariant filtering of signals that overlap with noise in both space and frequency can be inefficient. However, the signal and noise may be well separated in the joint space/spatial-frequency domain, Then, it is possibl e to benefit from the application of space/spatial frequency approaches, Pr ocessing based on these approaches can outperform space or frequency invari ant-based methods. To this aim the concept of nonstationary space-varying f iltering is introduced in this paper as an extension of the time-varying fi ltering concept. The filtering definitions are based on statistical average s, although the filtering should commonly be applied knowing only a single noisy signal realization. The procedures that can produce good estimates of quantities crucial for efficient filtering, based on a single noisy signal realization, are considered, Special attention has been paid to the region of support estimation and cross-term effects removal. The efficiency of th e proposed space/spatial-frequency filtering concept is tested on the signa l forms inspired by the interferograms in optics, including real images as disturbances. Examples demonstrate the superiority of the proposed filterin g over the space-invariant one for the considered type of signals and noise .