Search results for "Random loss"

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Whole mirror duplication-random loss model and pattern avoiding permutations

2010

International audience; In this paper we study the problem of the whole mirror duplication-random loss model in terms of pattern avoiding permutations. We prove that the class of permutations obtained with this model after a given number p of duplications of the identity is the class of permutations avoiding the alternating permutations of length p2+1. We also compute the number of duplications necessary and sufficient to obtain any permutation of length n. We provide two efficient algorithms to reconstitute a possible scenario of whole mirror duplications from identity to any permutation of length n. One of them uses the well-known binary reflected Gray code (Gray, 1953). Other relative mo…

[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]Class (set theory)0206 medical engineeringBinary number0102 computer and information sciences02 engineering and technology[ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]01 natural sciencesIdentity (music)Combinatorial problemsTheoretical Computer ScienceGray codeCombinatoricsPermutation[ INFO.INFO-BI ] Computer Science [cs]/Bioinformatics [q-bio.QM]Gene duplicationRandom loss[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]Pattern avoiding permutationGenerating algorithmComputingMilieux_MISCELLANEOUSMathematicsDiscrete mathematicsWhole duplication-random loss modelMathematics::CombinatoricsGenomeParity of a permutationComputer Science Applications[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][ INFO.INFO-CC ] Computer Science [cs]/Computational Complexity [cs.CC]Binary reflected Gray code010201 computation theory & mathematicsSignal Processing[INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM]020602 bioinformaticsAlgorithmsInformation Systems
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Application of Periodic Frames to Image Restoration

2014

In this chapter, we present examples of image restoration using periodic frames. Images to be restored were degraded by blurring, aggravated by random noise and random loss of significant number of pixels. The images are transformed by periodic frames designed in Sects. 17.2 and 17.4, which are extended to the 2D setting in a standard tensor product way. In the presented experiments, performances of different tight and semi-tight frames are compared between each other in identical conditions.

symbols.namesakeTensor productPixelComputer scienceTight frameRandom noiseRandom lossGaussian functionsymbolsAlgorithmInfinite impulse responseImage restoration
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