Local frames

Anthony Teolis; John J. Benedetto

doi:10.1117/12.162276

1 November 1993 Local frames

Anthony Teolis, John J. Benedetto

Proceedings Volume 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing; (1993) https://doi.org/10.1117/12.162276
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

In this paper we introduce the concept of a local Hilbert space frame and develop theory for the representation and reconstruction of signals using local frames. The theory of global frames is due to Duffin and Schaeffer. Local frames are defined with respect to a global frame and a particular element from a Hilbert space H. For any signal f* (epsilon) H, H may be decomposed into two signal dependent subspaces: a finite dimensional one which essentially contains the signal f* and one to which the signal is essentially orthogonal. The frame elements associated with the former subspace constitute the local frame around f*.

Citation Download Citation

Anthony Teolis and John J. Benedetto "Local frames", Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); https://doi.org/10.1117/12.162276

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