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Influence of GIBBS Phenomenon on the Mutual Coherence in Sparse Representations
Moscow University Computational Mathematics and Cybernetics. 2016. Vol. 40. P. 155–160.
Krylov A. S., Umnov A.
Translator: A. S. Krylov, Umnov A.
The influence of ringing effect (which is based on the Gibbs phenomenon) on the mutual coherence in sparse representation approach is considered. It is shown that for random vectors, the ringing effect increases the average mutual coherence. Numerical results that demonstrate that the mutual coherence behaves identically for real images are given. It is also shown how the ringing effect affects the sparsity of representations (which is closely related to the mutual coherence).
Kivalov S., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.
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Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
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Umnov A., Krylov A. S., Computer Optics 2016 Vol. 40 No. 6 P. 895–903
In this paper we suggest an algorithm for ringing suppression based on a sparse
representation method. As one of its steps, the suggested method includes image deblurring
based on the Wiener-Hunt deconvolution algorithm. The ringing suppression algorithm uses
the signals' mutual coherence and sparsities analysis when dealing with the ringing effect
based on the sparse representation method. We also ...
Added: October 21, 2017
Umnov A., Krylov A. S., Pattern Recognition and Image Analysis 2017 Vol. 27 No. 4 P. 754–762
In this work we discuss methods for image ringing detection and suppression that are based on the sparse representations approach and suggest a new ringing suppression method. The ringing detection algorithm is based on construction of the synthetic dictionary that is used to represent ringing effect as a sum of blurred edge and pure ringing ...
Added: October 17, 2017
Alexey V. Umnov, Krylov A., Nasonov A., Lecture Notes in Computer Science 2015 Vol. 9386 P. 35–45
The article refers to the problem of ringing artifact suppression. The ringing effect is caused by high-frequency information corruption or loss, it appears as waves or oscillations near strong edges. We propose a novel method for ringing artifact suppression after Fourier cut-off filtering. It can be also used for image deringing in the case of ...
Added: October 14, 2015
Umnov A., Nasonov A. V., Krylov A. S. et al., , in: 2014 12th International Conference on Signal Processing (ICSP).: United States of America: IEEE, 2014. P. 662–667.
The problem of non-reference ringing detection is considered. The idea of the proposed method is to decompose the input edges into the sums of blurred edge, ringing oscillations and the residual using sparse representation approach with the pre-generated dictionary. Edges with ringing effect are modeled by applying ideal low-pass filter to the step edge with ...
Added: March 1, 2015