Grassmannian Frames

Grassmannian Frames

In harmonic analysis, signal processing, and in related areas, there has been considerable interest in frames. Conceptually, frames provide generalized basis for overcomplete or redundant systems. Recently we have examined the problem of defining and constructing frames with certain nice properties. In the process, we created a class of frames that we define as Grassmannian frames. Essentially, Grassmannian frames are uniform frames that the minimize the maximum correlation over the class of uniform frames of fixed redundancy. The name “Grassmannian” comes from the natural relationship to packing lines in the Grassmann manifold. We have investigated both finite-dimensional and infinite-dimensional Grassmannian frames. Our results extend recent findings on uniform tight frames and have nice applications to wireless communication and multiple description coding.

Our results are summarized in:

T. Strohmer and R. W. Heath, Jr.Grassmannian Frames with Applications to Coding and Communications,” in Applied and Computational Harmonic AnalysisVol. 14, Issue 3, pp. 257-275, May 2003.

We are currently working on the problem of finding finite-dimensional Grassmannian frames. Our initial results are summarized in:

J. A. TroppI. DhillonR. W. Heath, Jr.,   T. StrohmerDesigning Structured Tight Frames Via An Alternating Projection Method,” The University of Texas at Austin, ICES Report 03-50, December 2003, also submitted to the IEEE Trans. on Info. Theory.

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