Learning the Right Model from the Data
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 d...
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| Autores principales: | , , |
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| Formato: | SER |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_22965009_v_n9780817637781_p325_Aldroubi |
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| Sumario: | 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. |
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