Proceedings PaperProcessing of compressed and encrypted imagery: complexity analyses with application to novel regimes of efficient computation
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Computational efficiencies can accrue from the processing of compressed imagery, due to an inherently reduced data burden. Since certain encryption schemes yield compressed ciphertext, computations over the range space of compressive or encryptive transformations can, in principle, exhibit computational advantages over the processing of uncompressed data or plaintext. We have recently elucidated theory fundamental to the processing of compressed and encrypted imagery, and have proposed general techniques for computation over well- known compressive formats. In this introductory paper, we analyze the efficiency of generalized operations over compressed data, with emphasis upon functions common to image and signal processing. Complexity theory derived from principles of sparse matrix processing is employed in the prediction of a critical compression ratio (CCR). Compression exceeding the CCR is required to achieve computational speedup within a given transformational regime. Additionally, given the compression ratio of a transform, as well as an image operation, we can predict the speedup of the corresponding operation over the transform's range space. Furthermore, we propose a novel computational paradigm which is based upon a network of transformations, and given optimization algorithms which determine the time-optimal computational path through such a network.