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Relevant bibliographies by topics / Gabor multiplier

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Academic literature on the topic 'Gabor multiplier'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Gabor multiplier"

1

BALAZS, PETER. "HILBERT–SCHMIDT OPERATORS AND FRAMES — CLASSIFICATION, BEST APPROXIMATION BY MULTIPLIERS AND ALGORITHMS." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 02 (2008): 315–30. http://dx.doi.org/10.1142/s0219691308002379.

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In this paper we deal with the theory of Hilbert–Schmidt operators, when the usual choice of orthonormal basis, on the associated Hilbert spaces, is replaced by frames. We More precisely, we provide a necessary and sufficient condition for an operator to be Hilbert–Schmidt, based on its action on the elements of a frame (i.e. an operator T is [Formula: see text] if and only if the sum of the squared norms of T applied on the elements of the frame is finite). Also, we construct Bessel sequences, frames and Riesz bases of [Formula: see text] operators using tensor products of the same sequences in the associated Hilbert spaces. We state how the [Formula: see text] inner product of an arbitrary operator and a rank one operator can be calculated in an efficient way; and we use this result to provide a numerically efficient algorithm to find the best approximation, in the Hilbert–Schmidt sense, of an arbitrary matrix, by a so-called frame multiplier (i.e. an operator which act diagonally on the frame analysis coefficients). Finally, we give some simple examples using Gabor and wavelet frames, introducing in this way wavelet multipliers.

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2

Gu, Qing, and Deguang Han. "Functional Gabor frame multipliers." Journal of Geometric Analysis 13, no. 3 (2003): 467–78. http://dx.doi.org/10.1007/bf02922054.

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3

Benedetto, John J., and Götz E. Pfander. "Frame expansions for Gabor multipliers." Applied and Computational Harmonic Analysis 20, no. 1 (2006): 26–40. http://dx.doi.org/10.1016/j.acha.2005.03.002.

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4

Feichtinger, H. G., M. Hampejs, and G. Kracher. "Approximation of Matrices by Gabor Multipliers." IEEE Signal Processing Letters 11, no. 11 (2004): 883–86. http://dx.doi.org/10.1109/lsp.2004.833581.

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5

Nazarkevych, Mariya, Yaroslav Voznyi, and Oksana Troyan. "GENERALIZING GABOR FILTERS BASED ON ATEB-FUNCTIONS." Cybersecurity: Education Science Technique, no. 4 (2019): 72–84. http://dx.doi.org/10.28925/2663-4023.2019.4.7284.

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Image filtering attempts to achieve greater resolution. There is a large number of filters that allows you to bring images with clear borders. In addition, noise is present when digitizing images. One of the most common types of filtering is the Gabor filter. It allows you to restore the image with the contour allocation at a certain frequency. Its core looks like elements of the Fourier basis, which is multiplied by Gaussian. The widespread use of Gabor filters for filtration is due to the fact that it gives a strong response at those points of the image where there is a component with local features of frequency in space and orientation. It is proposed to use the Ateb-Gabor filter, which greatly expands the well-known Gabor filter. The Ateb-Gabor filter combines all the properties of a harmonic function, which is multiplied by Gaussian. As a harmonic function, it is proposed to use the Ateb-functions that greatly extend the trigonometric effect. The developed filter is applied to the images. The Ateb-Gabor filter depends on the frequency and directions of the quasiperiodic structure of the image. Usually, to simplify the task, the average image frequency is calculated. It is unchanged at every point. Filtration of images is based on the generalized Ateb-Gabor filter. Influence of filtering parameters on images is investigated. The properties of periodic Ateb-functions are investigated. The value of the period from which the filtering results depend on is calculated. Ateb-Gabor filtering allowed for wider results than the classic Gabor filter. The one-dimensional Gabor filter based on the Ateb-functions gives the possibility to obtain more lenient or more convex forms of function at the maximum described in this study. In this way, filtration with a large spectrum of curves can be realized. This provides quick identification, since a more versatile kind of filtering has been developed.

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6

Cordero, Elena, Karlheinz Gröchenig, and Fabio Nicola. "Approximation of Fourier Integral Operators by Gabor Multipliers." Journal of Fourier Analysis and Applications 18, no. 4 (2012): 661–84. http://dx.doi.org/10.1007/s00041-011-9214-1.

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7

Li, Zhongyan, and Deguang Han. "Functional Matrix Multipliers for Parseval Gabor Multi-frame Generators." Acta Applicandae Mathematicae 160, no. 1 (2018): 53–65. http://dx.doi.org/10.1007/s10440-018-0194-x.

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8

Onchis, Darian M., and Simone Zappalà. "Realizable algorithm for approximating Hilbert–Schmidt operators via Gabor multipliers." Journal of Computational and Applied Mathematics 337 (August 2018): 119–24. http://dx.doi.org/10.1016/j.cam.2018.01.006.

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9

Diao, Yuanan, Deguang Han, and Zhongyan Li. "Gabor single-frame and multi-frame multipliers in any given dimension." Journal of Functional Analysis 280, no. 9 (2021): 108960. http://dx.doi.org/10.1016/j.jfa.2021.108960.

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10

Werther, T., A. Klotz, G. Kracher, et al. "CPR Artifact Removal in Ventricular Fibrillation ECG Signals Using Gabor Multipliers." IEEE Transactions on Biomedical Engineering 56, no. 2 (2009): 320–27. http://dx.doi.org/10.1109/tbme.2008.2003107.

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