Tight frames, partial isometries, and signal reconstruction

2013/08/23 by Au-Yeung, Enrico, Datta, Somantika
#42C15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1308.5028

Abstract

This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination of the elements in the original frame. Several examples are considered, such as a Fourier frame on a spiral. The procedure can be applied to the construction of Parseval frames for L²(B(0,R)), the space of square integrable functions whose domain is the ball of radius R. When a finite number of measurements are used to reconstruct a signal in L²(B(0,R)), error estimates arising from such approximation are discussed.

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