Quantized Frame Expansions with Erasures

By Vivek K Goyal, Jelena Kovacevic, Jonathan A. Kelner. 2001

566 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/47d649c68b677ae36bb26b4964e7771bc2825cbb

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In Applied Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

Tight Frames and Their Symmetries (2004, background): “There is another notion of equivalence of frames found in [ GKK01 ] and [F01], where j = U j in (2.6) is replaced by j = j U j for some scalar j of unit modulus.”
Ellipsoidal tight frames and projection decompositions of operators (2003, background): “ructure. Tight frames may be constructed having speciﬁed length, components having a predetermined sequence of norms, or with properties making them resilient to erasures. For examples, see [1], [2], [7], and [10]. One area of rapidly advancing research lies in describing tight frames in which all t”
Equal-Norm Tight Frames with Erasures (2003, methodology): “There is another general class of equal-norm tight frames (see [ 16 ]).”
History and Evolution of the Density Theorem for Gabor Frames (2007, background): “range of areas, including, for example, sampling theory [1], operator theory [100], nonlinear sparse approximation [84], pseudodifferential operators [94], wavelet theory [49], wireless communications [171], data transmission with erasures [83], signal processing [24], and quantum computing [58].”
GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION (2003, methodology): “Recently ﬁnite frames have been proposed for multiple description coding for erasure channels, see [21, 20, 6].”
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].”
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].”
Coefficient quantization for frames in Banach spaces (2007, unknown): “Since the sequence (xi) does not have to be (and usually is not) a basis for H , the representation of an x ∈ H as the sequence (〈xi, x〉)i=1 includes some redundancy, which, for example, can be used to correct errors in transmissions [13].”
Density, overcompleteness, and localization of frames (2006, background): “Frames were first introduced by Duffin and Schaeffer [DS52] in the context of nonharmonic Fourier series, and today frames play important roles in many applications in mathematics, science, and engineering, including time-frequency analysis [Gr¨ o01], internet coding [ GKK01 ], speech and music proc”
Directional multiresolution image representations (2002, methodology): “This follows from the result in [72] that with the additive white noise model for the coefficients, the tight frame is optimal among normalized frames in minimizing mean-squared error.”
Framing pyramids (2003, background): “Hence, for signals of finite length , the reconstruction mean squared error (MSE) is [19]”
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.”
Error correction via linear programming (2005, background): “[3, 6, 13, 29–32, 36] and the bibliography contained therein.”
Manifold structure of spaces of spherical tight frames (2003, background): “In the real case, we thereby reprove the result [7] that all such frames are equivalent to each other if one allows orthogonal transformations of R and negating some vectors; we also prove the analogous result in the complex case.”