Optimized frames and multi-dimensional challenges in time-frequency analysis. (English) Zbl 1297.42047
Summary: 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.
MSC:
| 42C15 | General harmonic expansions, frames |
| 65D99 | Numerical approximation and computational geometry (primarily algorithms) |
| 42C20 | Other transformations of harmonic type |
References:
| [1] | 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) · doi:10.1109/97.704972 |
| [2] | Bourouihiya, A.: The tensor product of frames. Sampl. Theory Sig. Image Process. 7(1), 65-76 (2008) · Zbl 1182.42029 |
| [3] | Christensen, O.: An Introduction to Frames and Riesz Bases: Applied and Numerical Harmonic Analysis. Birkh��user, Boston (2003) · Zbl 1017.42022 · doi:10.1007/978-0-8176-8224-8 |
| [4] | Christensen, O., Feichtinger, H., Paukner, S.: Gabor Analysis for Imaging. Handbook of Mathematical Methods in Imaging. Springer, Berlin (2010) |
| [5] | Cristobal, G., Navarro, R.: Space and frequency variant image enhancement based on a Gabor representation. Pattern Recogn. Lett. 15(3), 273-277 (1994) · Zbl 0802.68173 · doi:10.1016/0167-8655(94)90059-0 |
| [6] | 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) · Zbl 1196.65036 · doi:10.1016/j.cam.2010.05.010 |
| [7] | Feichtinger, H., Onchis, D., Ricaud, B., Torrésani, B., Wiesmeyr, C.: A method for optimizing the ambiguity function concentration. Proceedings of EUSIPCO (2012) · Zbl 1196.65036 |
| [8] | de Gosson, M.A., Onchis, D.: Multivariate symplectic Gabor frames with Gaussian windows. preprint (2012) |
| [9] | Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001) · Zbl 0966.42020 · doi:10.1007/978-1-4612-0003-1 |
| [10] | Kobarg, J., Dyatlov, A., Schiffler, S.: MALDI data preprocessing. Tech. Rep. 7, 1 (2011) |
| [11] | Lenstra, A.K., Lenstra, H.W., Lovàsz, H.W.: L. Factoring polynomials with rational coefficients. Math. Ann. 261, 515-534 (1982) · Zbl 0488.12001 · doi:10.1007/BF01457454 |
| [12] | 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) · Zbl 0770.30025 |
| [13] | 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) · Zbl 1042.65069 · doi:10.1016/S0377-0427(03)00549-1 |
| [14] | Qiu, S., Feichtinger, H.G.: Discrete Gabor structures and optimal representation. IEEE Trans. Sig. Process. 43(10), 2258-2268 (1995) · doi:10.1109/78.469862 |
| [15] | Seip, K., Wallstén, R.: Density theorems for sampling and interpolation in the Bargmann-Fock space. II, J. Reine Angew. Math. 429, 107-113 (1992) · Zbl 0745.46033 |
| [16] | Wang, Y., Chua, C.-S.: Face recognition from 2D and 3D images using 3D Gabor filters. Image Vis. Comput. 23(11), 1018-1028 (2005) · doi:10.1016/j.imavis.2005.07.005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
