{'fraction_non_alphanumeric': 0.018255578093306288, 'fraction_numerical': 0.0, 'mean_word_length': 5.675675675675675, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Nonlinear image filtering in a mixture of Gaussian and heavy-tailed noise

Inspired by robust estimation, nonlinear denoising methods combining the mean, the median, and the LogCauchy filters are proposed. Some statistical and asymptotic properties are studied, and comparisons with other nonlinear filtering schemes are performed. Experimental results showing a much improved performance of the proposed filters in the presence of Gaussian and heavy-tailed noise are analyzed and illustrated.