Artículo
Abstract:
In this chapter we discuss the problem of finding the shift-invariant space model that best fits a given class of observed data F. If the data is known to belong to a fixed—but unknown—shift-invariant space V(Φ) generated by a vector function Φ, then we can probe the data F to find out whether the data is sufficiently rich for determining the shift-invariant space. If it is determined that the data is not sufficient to find the underlying shift-invariant space V, then we need to acquire more data. If we cannot acquire more data, then instead we can determine a shift-invariant subspace S ⊂ V whose elements are generated by the data. For the case where the observed data is corrupted by noise, or the data does not belong to a shift-invariant space V(Φ), then we can determine a space V(Φ) that fits the data in some optimal way. This latter case is more realistic and can be useful in applications, e.g., finding a shift-invariant space with a small number of generators that describes the class of chest X-rays. © 2006, Birkhäuser Boston.
Registro:
| Documento: | Artículo |
| Título: | Learning the Right Model from the Data |
| Autor: | Aldroubi, A.; Cabrelli, C.; Molter, U. |
| Filiación: | Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Capital Federal, 1428, Argentina CONICET, Argentina |
| Palabras clave: | Class Versus; Optimal Space; Orthonormal Basis; Riesz Basis; Space Versus |
| Año: | 2006 |
| Número: | 9780817637781 |
| Página de inicio: | 325 |
| Página de fin: | 333 |
| DOI: | http://dx.doi.org/10.1007/0-8176-4504-7_14 |
| Título revista: | Applied and Numerical Harmonic Analysis |
| Título revista abreviado: | Appl. Numer. Harmon. Anal. |
| ISSN: | 22965009 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_22965009_v_n9780817637781_p325_Aldroubi |
Referencias:
- Aldroubi, A., Oblique projections in atomic spaces (1996) Proc. Amer. Math. Soc., 124, pp. 2051-2060
- Aldroubi, A., Cabrelli, C.A., Hardin, D., Molter, U.M., (2006) Optimal Shift-Invariant Spaces and Their Parseval Frame Generators
- Aldroubi, A., Cabrelli, C.A., Hardin, D., Molter, U., Rodado, A., Determining sets of shift invariant spaces (2003) Wavelets and Their Applications (Chennai, January 2002), pp. 1-8. , M. Krishna, R. Radha, and S. Thangavelu, eds., Allied Publishers, New Delhi
- Aldroubi, A., Gröchenig, K., Non-uniform sampling and reconstruction in shift-invariant spaces (2001) SIAM Review, 43, pp. 585-620
- Benedetto, J.J., Ferreira, P.J.S.G., (2001) Modern Sampling Theory: Mathematics and Applications, , Birkhäuser, Boston
- Benedetto, J.J., Zayed, A.I., (2004) Sampling, Wavelets, and Tomography, , Birkhäuser, Boston
- Cucker, F., Smale, S., On the mathematical foundations of learning (2002) Bull. Amer. Math. Soc. (N.S.), 39, pp. 1-49
- de Boor, C., de Vore, R., Ron, A., The structure of finitely generated shift-invariant subspaces of L2(Rd) (1994) J. Funct. Anal., 119, pp. 37-78
- Goodman, T.N.T., Lee, S.L., Tang, W.S., Wavelets in wandering subspaces (1993) Trans. Amer. Math. Soc., 338, pp. 639-654
Citas:
---------- APA ----------
Aldroubi, A., Cabrelli, C. & Molter, U. (2006) . Learning the Right Model from the Data. Applied and Numerical Harmonic Analysis(9780817637781), 325-333.http://dx.doi.org/10.1007/0-8176-4504-7_14
---------- CHICAGO ----------
Aldroubi, A., Cabrelli, C., Molter, U. "Learning the Right Model from the Data" . Applied and Numerical Harmonic Analysis, no. 9780817637781 (2006) : 325-333.http://dx.doi.org/10.1007/0-8176-4504-7_14
---------- MLA ----------
Aldroubi, A., Cabrelli, C., Molter, U. "Learning the Right Model from the Data" . Applied and Numerical Harmonic Analysis, no. 9780817637781, 2006, pp. 325-333.http://dx.doi.org/10.1007/0-8176-4504-7_14
---------- VANCOUVER ----------
Aldroubi, A., Cabrelli, C., Molter, U. Learning the Right Model from the Data. Appl. Numer. Harmon. Anal. 2006(9780817637781):325-333.http://dx.doi.org/10.1007/0-8176-4504-7_14
