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 possible to benefit from the application of space/spatial frequency approaches. Processing based on these approaches can outperform space or frequency invariant-based methods. To this aim the concept of nonstationary space-varying filtering is introduced in this paper as an extension of the time-varying filtering concept. The filtering definitions are based on statistical averages, 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 the proposed space/spatial-frequency filtering concept is tested on the signal forms inspired by the interferograms in optics, including real images as disturbances. Examples demonstrate the superiority of the proposed filtering over the space-invariant one for the considered type of signals and noise.