In:
International Journal of Wavelets, Multiresolution and Information Processing, World Scientific Pub Co Pte Ltd, Vol. 03, No. 03 ( 2005-09), p. 347-359
Abstract:
We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinte-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and the corresponding positive operators for which this geometrical interpretation applies.
Type of Medium:
Online Resource
ISSN:
0219-6913
,
1793-690X
DOI:
10.1142/S0219691305000890
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2005
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