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2008
IEEE

Frames for linear reconstruction without phase

9 years 4 months ago
Frames for linear reconstruction without phase
Abstract— The objective of this paper is the linear reconstruction of a vector, up to a unimodular constant, when all phase information is lost, meaning only the magnitudes of frame coefficients are known. Reconstruction algorithms of this type are relevant for several areas of signal communications, including wireless and fiber-optical transmissions. The algorithms discussed here rely on suitable rank-one operator valued frames defined on finite-dimensional real or complex Hilbert spaces. Examples of such operator-valued frames are the rank-one Hermitian operators associated with vectors from maximal sets of equiangular lines or maximal sets of mutually unbiased bases. A more general type of examples is obtained by a tensor product construction. We also study erasures and show that in addition to loss of phase, a maximal set of mutually unbiased bases can correct for erased frame coefficients as long as no more than one erasure occurs among the coefficients belonging to each b...
Bernhard G. Bodmann, Peter G. Casazza, Dan Edidin,
Added 29 May 2010
Updated 29 May 2010
Type Conference
Year 2008
Where CISS
Authors Bernhard G. Bodmann, Peter G. Casazza, Dan Edidin, Radu Balan
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