{'fraction_non_alphanumeric': 0.013761467889908258, 'fraction_numerical': 0.0, 'mean_word_length': 5.616161616161616, '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}}
Multidimensional Unlimited Sampling: A Geometrical Perspective

The recently introduced unlimited sampling theorem proves that a one-dimensional bandlimited function can be perfectly recovered from a constant factor oversampling of its modulo samples. The advantage of this approach is that arbitrary high-dynamic-range signals can be recovered without sensor saturation or clipping. In this paper, we prove a multidimensional version of the unlimited sampling theorem that works with arbitrary sampling lattices. We also present a geometrical perspective on the emerging class of modulo sampling problem that is based on the topology of quotient spaces.