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This paper introduces a new algorithm for the so-called "Analysis Problem" in quantization of finite frame representations which provides a near-optimal solution in the case of random measurements.
On the β \beta -expansions of real numbers
W. Parry · 1960
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A. Edelman · 1988
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I. Galton and H.T. Jensen · 1996
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Lower bound on the mean-squared error in oversampled quantization of periodic signals using vector quantization analysis
N.T. Thao and M. Vetterli · 1996
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Quantized overcomplete expansions in ℝ N \mathbb{R}^{N} : analysis, synthesis, and algorithms
V.K. Goyal, M. Vetterli, and N.T. Thao · 1998
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Geometric discrepancy
J. Matoušek · 1999
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Local operator theory, random matrices and Banach spaces
K.R. Davidson and S.J. Szarek · 2001
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The discrepancy method: randomness and complexity
B. Chazelle · 2002
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Ergodic theory of numbers
K. Dajani and C. Kraaikamp · 2002
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Addenda and corrigenda to: “Local operator theory, random matrices and Banach spaces”
K.R. Davidson and S.J. Szarek · 2003
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One-bit sigma-delta quantization with exponential accuracy
C.S. Güntürk · 2003
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Second-order sigma-delta ( Σ Δ ) (\Sigma\Delta) quantization of finite frame expansions
J.J. Benedetto, A.M. Powell, and Ö. Yılmaz · 2006
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Sigma-delta quantization and finite frames
J.J. Benedetto, A.M. Powell, and Ö. Yılmaz · 2006
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A/D conversion with imperfect quantizers
I. Daubechies, R.A. DeVore, C.S. Güntürk, and V.A. Vaishampayan · 2006
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Frame paths and error bounds for sigma-delta quantization
B.G. Bodmann and V.I. Paulsen · 2007
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On quantization of finite frame expansions: sigma-delta schemes of arbitrary order
M.C. Lammers, A.M. Powell, and Ö. Yılmaz · 2007
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Non-asymptotic theory of random matrices: extreme singular values
M. Rudelson and R. Vershynin · 2010
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An optimal family of exponentially accurate one-bit sigma-delta quantization schemes
P. Deift, F. Krahmer, and C.S. Güntürk · 2011
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Mathematics of analog-to-digital conversion
C.S. Güntürk · 2012
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Approximation by Quantized Sums
V. Molino · 2012
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Introduction to the non-asymptotic analysis of random matrices
R. Vershynin · 2012
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Sobolev duals for random frames and Σ Δ \Sigma\Delta quantization of compressed sensing measurements
C. S. Güntürk, M. Lammers, A. M. Powell, R. Saab, and Ö. Yılmaz · 2013
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On optimal perfect reconstruction feedback quantizers
M.S. Derpich, E.I. Silva, D.E. Quevedo, and G.C. Goodwin · 2008
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Smallest singular value of a random rectangular matrix
M. Rudelson and R. Vershynin · 2009
Cited alongside, same era.
Sobolev duals in frame theory and sigma-delta quantization
J. Blum, M. Lammers, A.M. Powell, and Ö. Yılmaz · 2010
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Alternative dual frames for digital-to-analog conversion in sigma-delta quantization
M. Lammers, A.M. Powell, and Ö. Yılmaz · 2010
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Near-optimal encoding for sigma-delta quantization of finite frame expansions
M. Iwen and R. Saab · 2013
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Quantization and finite frames
A.M. Powell, R. Saab, and Ö. Yılmaz · 2013
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Exponential decay of reconstruction error from binary measurements of sparse signals
R.G. Baraniuk, S. Foucart, D. Needell, Y. Plan, and M. Wootters · 2014
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Sigma-delta quantization of sub-gaussian frame expansions and its application to compressed sensing
F. Krahmer, R. Saab, and Ö. Yılmaz · 2014
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