Abstract
The aim of this introductory communication is to present some challenges of the emerging research topics related to uncertainties, optimizations and multi-dimensional settings in the framework of time-frequency analysis. On one hand we study problems related to multivariate high-D Gabor frame constructions and on the other hand we corelate them with the optimal window constructions.
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Bastiaans, M.J., van Leest, A.J.: From the rectangular to the quincunx Gabor lattice via fractional fourier transformation. IEEE Sig. Proc. Lett. 5(8), 203–205 (1998)
Bourouihiya, A.: The tensor product of frames. Sampl. Theory Sig. Image Process. 7(1), 65–76 (2008)
Christensen, O.: An Introduction to Frames and Riesz Bases: Applied and Numerical Harmonic Analysis. Birkhäuser, Boston (2003)
Christensen, O., Feichtinger, H., Paukner, S.: Gabor Analysis for Imaging. Handbook of Mathematical Methods in Imaging. Springer, Berlin (2010)
Cristobal, G., Navarro, R.: Space and frequency variant image enhancement based on a Gabor representation. Pattern Recogn. Lett. 15(3), 273–277 (1994)
Feichtinger, H.G., Onchis, D.: Constructive realization of dual systems for generators of multi-window spline-type spaces. J. Comput. Appl. Math. 234(12), 3467–3479 (2010)
Feichtinger, H., Onchis, D., Ricaud, B., Torrésani, B., Wiesmeyr, C.: A method for optimizing the ambiguity function concentration. Proceedings of EUSIPCO (2012)
de Gosson, M.A., Onchis, D.: Multivariate symplectic Gabor frames with Gaussian windows. preprint (2012)
Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001)
Kobarg, J., Dyatlov, A., Schiffler, S.: MALDI data preprocessing. Tech. Rep. 7, 1 (2011)
Lenstra, A.K., Lenstra, H.W., Lovàsz, H.W.: L. Factoring polynomials with rational coefficients. Math. Ann. 261, 515–534 (1982)
Lyubarskii, Y.I.: Frames in the Bargmann space of entire functions. In: Entire and Subharmonic Functions, Adv. Soviet Math., vol. 11, pp. 167–180. Amer. Math. Soc., Providence. Mathematical Reviews (MathSciNet): MR1188007 (1992)
Mikula, K., Sgallari, F.: Semi-implicit finite volume scheme for image processing in 3D cylindrical geometry. J. Comput. Appl. Math. 161(1), 119–132 (2003)
Qiu, S., Feichtinger, H.G.: Discrete Gabor structures and optimal representation. IEEE Trans. Sig. Process. 43(10), 2258–2268 (1995)
Seip, K., Wallstén, R.: Density theorems for sampling and interpolation in the Bargmann–Fock space. II, J. Reine Angew. Math. 429, 107–113 (1992)
Wang, Y., Chua, C.-S.: Face recognition from 2D and 3D images using 3D Gabor filters. Image Vis. Comput. 23(11), 1018–1028 (2005)
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Communicated by: Peter Maass, Hans G. Feichtinger, Bruno Torresani, Darian M. Onchis, Benjamin Ricaud and David Shuman
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Onchis, D.M. Optimized frames and multi-dimensional challenges in time-frequency analysis. Adv Comput Math 40, 703–709 (2014). https://doi.org/10.1007/s10444-013-9332-1
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DOI: https://doi.org/10.1007/s10444-013-9332-1