{'fraction_non_alphanumeric': 0.018579234972677595, 'fraction_numerical': 0.0, 'mean_word_length': 5.361111111111111, '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}}
Construction of Binary Sensing Matrices Using Extremal Set Theory

The construction of binary sensing matrices is one of the active directions in the emerging field of compressed sensing (CS). Due to their sparse structure and competitive performance, they provide multiplier-less and faster dimensionality reduction in applications such as data compression. This letter attempts to relate the notion of extremal set theory to the construction of good CS matrices. In particular, we show that extremal set theory is useful for constructing binary sensing matrices and bounding their maximum column size (i.e., number of columns). We also prove the existence of binary sensing matrices whose column size meets the upper bound. Simulation results show that the constructed matrices outperform Gaussian and Bernoulli random matrices, as well as other deterministic binary and bipolar constructions from the literature.