17-01-2019 дата публикации
Номер: US20190020906A1
Digital files are compressed using a process including Schmidt decompositions of matrices using an algorithm, termed ‘BSD’ herein, which is based on an algebraic method generalizing QR decomposition. Software analyzes an input file and initially identifies a matrix M, with entries within a predefined set of integers, within the file. Next, essential entries are defined, extracted from M, that contain sufficient information to recover M using BSD. The compressed file includes the essential entries and their positions within M. To achieve an encryption process, software encrypts the pattern matrix that includes the positions of the essential entries of M. To achieve a lossy compression, software identifies essential entries that contain sufficient information to recover an approximation to M for which the quality is determined by an error threshold. For a more efficient lossy compression, software uses singular value decomposition, BSD, and other signal processing of M. 1. A method for encoding digital data , comprising: use SVD to find Ma, an mn×pq matrix, with the lowest Schmidt rank R for which PSNR(Ma, M)≥a predetermined value;', 'quantize Ma to find a matrix Q whose entries are integers;', 'define a left essential matrix A;', 'define a right essential matrix B;', 'define a pattern matrix P for storing positions of essential entries;', {'sub': 'e', 'assign to matrix Ma starting value of Q;'}, {'sub': 'e', 'define a matrix A;'}, {'sub': 'e', 'define a matrix B,'}, 'assign a starting value to e;', {'sub': e', 'e, 'a) select a non-zero entry dof M;'}, {'sub': 'e', 'sup': 'th', 'b) store the position (r, c) of the selected non-zero entry of Mat an ecolumn of P;'}, {'sub': e', 'e', 'e', 'e', 'e', 'e', 'e, 'c) select from Mtwo matrices Aand Bhaving das a common entry and for which A⊗B/dis a term in the Schmidt decomposition of M with respect to the parameters m, n, p, and q;'}, {'sup': 'th', 'sub': e', 'e, 'd) store in the em×p block of A the entries of M whose ...
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