Optimal frames for erasures

By Roderick B Holmes, Vern I. Paulsen. 2004

388 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/6924e4a1b4ddb8770e0ac5e5a4a5b0c525775acb

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Ellipsoidal tight frames and projection decompositions of operators (2003, background): “[10] Casazza and Leon have shown in [3] the existence of “spherical frames for R with a given frame operator”, which is an equivalent problem.”
Construction, classification and parametrization of complex Hadamard matrices (2011, background): “[12], [23], [46], [53] and [117]) as they have applications in coding [65] and quantum information theory [122].”
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].”
GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION (2003, background): “(ii) Holmes and Paulsen have shown that Grassmannian frames are optimal with respect to u erasures [27].”
Steiner equiangular tight frames (2010, background): “This Gram representation of an ETF has the additional benefit of being invariant with respect to rotations of the frame elements themselves, and, in the real-variable case, is closely-related to the incidence matrix of the corresponding strongly regular graph [16].”
Linear Independence of Gabor Systems in Finite Dimensional Vector Spaces (2005, background): “For more, see [7, 9, 15] and the references cited therein.”
On the existence of equiangular tight frames (2007, methodology): “In particular, Holmes and Paulsen have shown that an ETF provides an error-correcting code that is maximally robust against two erasures [9].”
Encoded distributed optimization (2017, background): “1Performance of frames under erasures have been studied in [7], [8], though not in the context of convex optimization.”
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.”
A note on equiangular tight frames (2008, neutral): “We insert (7) into (6) and obtain G∗G = n− 1 n ( Φ∗Φ + Φfnf ∗ nΦ ) .”
The road to equal-norm Parseval frames (2010, methodology): “Problem 2.5 (V. Paulsen).”
Manifold structure of spaces of spherical tight frames (2003, background): “inner–product preserving transformations OE n of the Hilbert space En. (Thus, OR n is the group of n×northogonal matrices, and OC n is the group of n× nunitary matrices.) It is well known (cf [2] and [8]) that GE k,n can be naturally identiﬁed with the subset of the Grassman manifold of n–planes in ”
On the construction of equiangular frames from graphs (2009, background): “This is the type III equivalence of [ HP04 ] (without reordering).”