Optimal noise suppression: A geometric nature of pseudoframes for subspaces |
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Authors: | Shidong Li Hidemitsu Ogawa |
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Institution: | (1) Department of Mathematics, San Francisco State University, San Francisco, CA 94132, USA;(2) Department of Computer Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku Tokyo, 152-8552, Japan |
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Abstract: | Pseudoframes for subspaces (PFFS) is a notion of frame-like expansions for a subspace in a separable Hilbert space 11]. The spanning nature of the sequences and in a PFFS (relative to the subspace ) is generally very different from that of a frame. Incidentally, a PFFS constitutes generally a nonorthogonal projections
onto . The directions of the projection determine the geometric meanings and its applications of a PFFS. PFFS also provides a means
for the construction of nonorthogonal projections that arises in various linear reconstruction problems. This article is aimed
at elaborations on such geometrical properties, demonstration of natural needs of nonorthogonal projections in applications
and how PFFS can be applied, particularly for optimal noise suppressions. In this specific application, we show that PFFS
is not only natural and sufficient but also necessary for generating an optimal solution among the class of all linear and
series-based methods.
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Keywords: | pseudoframes for subspaces frames nonorthogonal projections optimal noise suppression |
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