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Journal articles on the topic 'Gabor multiplier'

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Published: 25 May 2024

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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 (March 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 (September 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 (January 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 (November 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 (January 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 (June 28, 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 (May 2021): 108960. http://dx.doi.org/10.1016/j.jfa.2021.108960.

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10

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

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11

Gröchenig, Karlheinz. "Representation and approximation of pseudodifferential operators by sums of Gabor multipliers." Applicable Analysis 90, no. 3-4 (March 2011): 385–401. http://dx.doi.org/10.1080/00036811.2010.499507.

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12

Pandey, S. S. "Gabor multipliers for weighted Banach spaces on locally compact abelian groups." Journal of Mathematics of Kyoto University 49, no. 2 (2009): 235–54. http://dx.doi.org/10.1215/kjm/1256219154.

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13

Hamada, T., K. Kato, and M. Yamashima. "A Ring Model for Direction-Selective Simple Cells in the Visual Cortex." Perception 26, no. 1_suppl (August 1997): 164. http://dx.doi.org/10.1068/v970164.

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Experimental studies have shown that (1) direction-selective simple cells in the visual cortex have spatiotemporally inseparable receptive fields, whose spatial profiles at a given time are described by Gabor functions: a sinusoid multiplied by a Gaussian, with a phase parameter; (2) among simple cells, the phases are distributed not merely at 0 and pi/2 as for sine and cosine Gabor functions, but uniformly between 0 and 2pi (DeAngelis et al, 1993 Journal of Neurophysiology69 1091 – 1117); (3) anatomically, these simple cells receive inputs more from other cortical cells than from the lateral geniculate body (LGN) (Ahmed et al, 1994 Journal of Comparative Neurology341 39 – 49). We accordingly propose here a neural model for the simple cells whose receptive fields are assumed to be of the same spatial position and orientation. In the model, several cortical cells are arranged in a ring with mutual excitatory and inhibitory connections, and receive afferent signals from lagged and nonlagged cells in LGN (Saul and Humphrey, 1990 Journal of Neurophysiology64 206 – 224). Computer simulation shows that the cortical cells have spatiotemporally inseparable receptive fields with spatial profiles described by Gabor functions, and are directionally selective to a moving grating. The cells are found to be arranged so that their Gabor phases vary regularly from 0 to 2pi with rotation along the ring. The connection among the cortical cells has a role of amplification as in the canonical microcircuit model (Douglas et al, 1989 Neural Computation1 480 – 488).

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14

Dörfler, Monika, and Bruno Torrésani. "Representation of Operators in the Time-Frequency Domain and Generalized Gabor Multipliers." Journal of Fourier Analysis and Applications 16, no. 2 (August 4, 2009): 261–93. http://dx.doi.org/10.1007/s00041-009-9085-x.

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15

Rachdi, Lakhdar T., and Samia Sghaier. "The windowed Fourier transform and Gabor multipliers associated with the Riemann-Liouvlle transform." Integral Transforms and Special Functions 30, no. 7 (March 26, 2019): 564–80. http://dx.doi.org/10.1080/10652469.2019.1593408.

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16

BALAZS, PETER, JEAN-PIERRE ANTOINE, and ANNA GRYBOŚ. "WEIGHTED AND CONTROLLED FRAMES: MUTUAL RELATIONSHIP AND FIRST NUMERICAL PROPERTIES." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 01 (January 2010): 109–32. http://dx.doi.org/10.1142/s0219691310003377.

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Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while offering a numerical advantage in the sense of preconditioning. Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally, we analyze weighted frames numerically. First, we investigate three possibilities for finding weights in order to tighten a given frame, i.e. decrease the frame bound ratio. Then, we examine Gabor frames and how well the canonical dual of a weighted frame is approximated by the inversely weighted dual frame.

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17

Gao, Ruiqi, Jianwen Xie, Siyuan Huang, Yufan Ren, Song-Chun Zhu, and Ying Nian Wu. "Learning V1 Simple Cells with Vector Representation of Local Content and Matrix Representation of Local Motion." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6674–84. http://dx.doi.org/10.1609/aaai.v36i6.20622.

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This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of local contents of images and (2) the matrix representations of local pixel displacements caused by the relative motions between the agent and the objects in the 3D scene. When the image frame undergoes changes due to local pixel displacements, the vectors are multiplied by the matrices that represent the local displacements. Thus the vector representation is equivariant as it varies according to the local displacements. Our experiments show that our model can learn Gabor-like filter pairs of quadrature phases. The profiles of the learned filters match those of simple cells in Macaque V1. Moreover, we demonstrate that the model can learn to infer local motions in either a supervised or unsupervised manner. With such a simple model, we achieve competitive results on optical flow estimation.

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18

Tariq, Umair, Zonghai Hu, Rokham Tariq, Muhammad Shahid Iqbal, and Muhammad Sadiq. "High-Performance Embedded System for Offline Signature Verification Problem Using Machine Learning." Electronics 12, no. 5 (March 4, 2023): 1243. http://dx.doi.org/10.3390/electronics12051243.

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This paper proposes a high-performance embedded system for offline Urdu handwritten signature verification. Though many signature datasets are publicly available in languages such as English, Latin, Chinese, Persian, Arabic, Hindi, and Bengali, no Urdu handwritten datasets were available in the literature. So, in this work, an Urdu handwritten signature dataset is created. The proposed embedded system is then used to distinguish genuine and forged signatures based on various features, such as length, pattern, and edges. The system consists of five steps: data acquisition, pre-processing, feature extraction, signature registration, and signature verification. A majority voting (MV) algorithm is used for improved performance and accuracy of the proposed embedded system. In feature extraction, an improved sinusoidal signal multiplied by a Gaussian function at a specific frequency and orientation is used as a 2D Gabor filter. The proposed framework is tested and compared with existing handwritten signature verification methods. Our test results show accuracies of 66.8% for ensemble, 86.34% for k-nearest neighbor (KNN), 93.31% for support vector machine (SVM), and 95.05% for convolutional neural network (CNN). After applying the majority voting algorithm, the overall accuracy can be improved to 95.13%, with a false acceptance rate (FAR) of 0.2% and a false rejection rate (FRR) of 41.29% on private dataset. To test the generalization ability of the proposed model, we also test it on a public dataset of English handwritten signatures and achieve an overall accuracy of 97.46%.

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19

Guo, Gaoshan, Stéphane Operto, Ali Gholami, and Hossein S. Aghamiry. "Time-domain extended-source full-waveform inversion: algorithm and practical workflow." GEOPHYSICS, October 30, 2023, 1–94. http://dx.doi.org/10.1190/geo2023-0055.1.

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Extended-source full-waveform inversion (ES-FWI) first computes wavefields with data-driven source extensions such that the simulated data in inaccurate velocity models match the observed counterpart well enough to prevent cycle skipping. Then, the source extensions are minimized to update the model parameters toward the true medium. This two-step workflow is iterated until both data and sources are matched. It was recently shown that the source extensions are the least-squares solutions of the scattered data fitting problem. As a result, the source extensions are computed by propagating backward in time the deconvolved data residuals by the damped data-domain Hessian of the scattered data fitting problem. Estimating these weighted data residuals is the main computational bottleneck of time-domain ES-FWI. To mitigate this burden, we approximate the inverse data-domain Hessian by mono- and multi-dimensional matching filters with two simulations per source. We implement time-domain ES-FWI with the alternating-direction method of multiplier and total-variation regularization. Moreover, we apply ES-FWI with a multiscale approach involving frequency continuation and layer-stripping, with the latter being implemented with an offset-time dependent weighting operator. In this framework, we further regularize the inversions while mitigating their computational burden by matching the grid interval to the frequency bandwidth. Finally, the overall workflow combines ES-FWI and classical FWI during the early and late stages of the multiscale approach, respectively. We illustrate that the sensitivity of ES-FWI to the accuracy of the approximated inverse data-domain Hessian depends on the complexity of the targeted model, the data anatomy, and the accuracy of the starting model. In the case of the 2004 BP salt model, we demonstrate that the layer stripping is necessary when the inverse data-domain Hessian is approximated by a 2D Gabor matching filter and the starting model is crude, while this feature is not necessary with the Marmousi II model.

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20

Rachdi, Lakhdar T., and Besma Amri. "Gabor multipliers associated with the Bessel–Kingman hypergroup." Journal of Pseudo-Differential Operators and Applications 12, no. 3 (July 27, 2021). http://dx.doi.org/10.1007/s11868-021-00415-w.

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21

Skrettingland, Eirik. "Quantum Harmonic Analysis on Lattices and Gabor Multipliers." Journal of Fourier Analysis and Applications 26, no. 3 (June 2020). http://dx.doi.org/10.1007/s00041-020-09759-1.

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22

Kreme, Marina Ama, Valentin Emiya, Caroline Chaux, and Bruno Torresani. "Time-frequency fading algorithms based on Gabor multipliers." IEEE Journal of Selected Topics in Signal Processing, 2020, 1. http://dx.doi.org/10.1109/jstsp.2020.3045938.

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23

Yang, Ming, and Yun-Zhang Li. "Gabor frame multipliers and Parseval duals on the half real line." International Journal of Wavelets, Multiresolution and Information Processing, January 25, 2024. http://dx.doi.org/10.1142/s0219691324500036.

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24

Rahim, Naheean. "Design of a Modified Gabor Filter with Vedic Multipliers Using Verilog HDL." International Journal of Information and Electronics Engineering 5, no. 5 (2015). http://dx.doi.org/10.7763/ijiee.2015.v5.559.

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25

Knutsen, Helge. "A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers." Applied and Computational Harmonic Analysis, October 2022. http://dx.doi.org/10.1016/j.acha.2022.10.001.

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26

Knutsen, Helge. "A Fractal Uncertainty Principle for the Short-Time Fourier Transform and Gabor Multipliers." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4089331.

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27

Obiakara, Maxwell, Peter Etaware, and Kanayo Chukwuka. "Maximum Entropy Niche Modelling to Estimate the Potential Distribution of Phytophthora megakarya (Brasier & M. J. Griffin) in Tropical Regions." European Journal of Ecology 6, no. 2 (January 11, 2021). http://dx.doi.org/10.17161/eurojecol.v6i2.13802.

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Background: Phytophthora megakarya is an invasive pathogen endemic to Central and West Africa. This species causes the most devastating form of black pod disease. Despite the deleterious impacts of this disease on cocoa production, there is no information on the geographic distribution of P. megakarya. Aim: In this study, we investigated the potential geographic distribution of P. megakarya in cocoa-producing regions of the world using ecological niche modelling. Methods: Occurrence records of P. megakarya in Central and West Africa were compiled from published studies. We selected relevant climatic and edaphic predictor variables in the indigenous range of this species to generate 14 datasets of climate-only, soil-only, and a combination of both data types. For each dataset, we calibrated 100 candidate MaxEnt models using 20 regularisation multiplier values and five feature classes. The best model was selected from statistically significant candidates with an omission rate ≤ 5% and the lowest Akaike Information Criterion corrected for small sample sizes, and projected onto cocoa-producing regions in Southeast Asia, Central and South America. The risk of extrapolation in model transfer was measured using the mobility-oriented parity (MOP) metric. Results: We found an optimal goodness-of-fit and complexity for candidate models incorporating both climate and soil data. Predictions of the model with the best performance showed that nearly all of Central Africa, especially areas in Gabon, Equatorial Guinea, and southern Cameroon are at risk of black pod disease. In West Africa, suitable environments were observed along the Atlantic coast, from southern Nigeria to Gambia. Our analysis suggested that P. megakarya is capable of subsisting outside its native range, at least in terms of climatic and edaphic factors. Model projections identified likely suitable areas, especially in Brazil and Colombia, from southwestern Mexico down to Panama, and across the Caribbean islands in the Americas, and in Sri Lanka, Indonesia, Malaysia, and Papua New Guinea in Asia and adjacent areas Conclusion: The outcomes of this study would be useful for developing measures aimed at preventing the spread of this pathogen in the tropics.

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