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Characterization of Oblique Dual Frame Pairs

  • Yonina C. EldarEmail author
  • Ole Christensen
Open Access
Research Article
Part of the following topical collections:
  1. Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory

Abstract

Given a frame for a subspace Open image in new window of a Hilbert space Open image in new window , we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace Open image in new window . In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a general frame on an arbitrary Hilbert space, and then specialize the results to shift-invariant frames with multiple generators. In particular, we present explicit versions of our general conditions for the case of shift-invariant spaces with a single generator. The theory is also adapted to the standard frame setting in which the original and dual frames are defined on the same space.

Keywords

Hilbert Space Information Technology General Condition Single Generator Quantum Information 

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Copyright information

© Eldar and Christensen. 2006

Authors and Affiliations

  1. 1.Department of Electrical EngineeringTechnion – Israel Institute of TechnologyTechnion CityIsrael
  2. 2.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark

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