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Characterization of Oblique Dual Frame Pairs

Abstract

Given a frame for a subspace of a Hilbert space, we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace. 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.

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Correspondence to Yonina C. Eldar.

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Eldar, Y.C., Christensen, O. Characterization of Oblique Dual Frame Pairs. EURASIP J. Adv. Signal Process. 2006, 092674 (2006). https://doi.org/10.1155/ASP/2006/92674

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Keywords

  • Hilbert Space
  • Information Technology
  • General Condition
  • Single Generator
  • Quantum Information