{'fraction_non_alphanumeric': 0.035110533159947985, 'fraction_numerical': 0.0, 'mean_word_length': 4.9689922480620154, '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}}
On the Properties of a Relative Entropy Functional

The identification of the noise correlations (e.g., between the sensors of an array) is an important problem. It is also ill posed unless some additional conditions are verified. Here, these supplementary conditions are reduced to a low-rank hypothesis and to the knowledge (e.g., an upper bound of its length) of the general structure of the noise correlations. By introducing an original functional (named relative entropy functional), we develop a new approach for solving the above problem. In particular, it is shown that this functional inherits from its definition interesting and useful properties (such as location of the extrema, concavity, etc.). These properties are shown using elementary linear algebra.