L-statistics based space/spatial-frequency filtering of 2D signals in heavy tailed noise

•L-estimate space/spatial-frequency filtering is introduced for 2D signals in strong impulsive or mixed noise.•The three-component filtering consists of combined space/spatial-frequency α-trimmed and mean filter, and additional support function which selects dominant components.•The proposed procedure is designed for different 2D signals with fast-varying details and structures (interferograms, textures and surface images).•The filtering results are improved in terms of PSNR and visual quality compared to numerous existing filtering techniques.

Most of the commonly used stationary filtering techniques, performed either in the spatial or frequency domains, fail to produce good results for noisy signals with fast varying non-stationary structures. The filtering results could be improved by using space/spatial-frequency based non-stationary filters. Hence, a robust approach to space/spatial-frequency analysis of two-dimensional noisy signals is proposed in this paper. It is based on the two-dimensional L-estimate forms of the short-time Fourier transform, the spectrogram and the S-method. The proposed space/spatial-frequency distributions are used to define the L-estimate space-varying filtering procedure. It is designed for denoising of 2D non-stationary signals affected by the strong impulsive or mixed heavy-tailed and Gaussian noise. The efficiency of the proposed procedure is tested on the examples with interferogram-like images, textures and satellite images.