Equal-Norm Tight Frames with Erasures

By Peter G. Casazza, Jelena Kovacevic. Advances in Computational Mathematics, 2003

396 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/80b86cec9a7063e4ac2e53a5b236fb112f3cba40

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In Applied Mathematics

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Citations in the corpus

On the existence of equiangular tight frames (2007, background): “Two ETFs are calledframe equivalent if one can be transformed into the other by a sequence of these basic operations [3].”
Gabor Frames in Finite Dimensions (2013, methodology): “(See, for example, the conclusions section in [18].”
Encoded distributed optimization (2017, background): “1Performance of frames under erasures have been studied in [7], [8], though not in the context of convex optimization.”
Minimization of the probabilistic p-frame potential (2010, background): “For instance, a special class called finite unit norm tight frames (FUNTFs) that provide a Parseval-type representation very similar to orthonormal bases, has been customized to model data transmissions [6, 20].”
An Introduction to Frames (2008, background): “The redundant counterpart of a basis is called a frame.1 It is generally acknowledged2 that frames were born in 1952 in the work of Duffin and Schaeffer [78].”
Designing structured tight frames via an alternating projection method (2005, background): “Indeed, it is known that (modulo rotations) there exists a unique tight frame of vectors in -dimensional space [53, p. 13].”
Error correction via linear programming (2005, methodology): “Hence, (P 1 ) is an LP with inequality constraints and can be solved efficiently using standard or specialized optimization algorithms , see [4], [5].”
On some identities and inequalities for frames in Hilbert spaces (2006, methodology): “application in image processing [13], robust transmission over the Internet and wireless [11,29, 32], coding and communication [26,34] were given.”
Duality Principles in Frame Theory (2004, methodology): “For example, frames are now used to mitigate the effect of losses in packet-based communication systems and hence to improve the robustness of data transmission [10, 4], and to design high-rate constellations with full diversity in multiple-antenna code design [12].”
Frames of subspaces (2003, methodology): “For example, besides traditional applications as signal processing, image processing, data compression, and sampling theory, frames are now used to mitigate the effect of losses in packet-based communication systems and hence to improve the robustness of data transmission [7, 15], and to design high”