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- John J. Benedetto, Özgür Yilmaz, Alexander M. Powell
- 2004 IEEE International Conference on Acoustics…
- 2004

It is shown that sigma-delta (/spl Sigma//spl Delta/) algorithms can be used effectively to quantize finite frame expansions for R/sup d/. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that /spl Sigma//spl Delta/ quantizers outperform the standard PCM schemes.

- C. Sinan Güntürk, Mark Lammers, Alexander M. Powell, Rayan Saab, Özgür Yilmaz
- Foundations of Computational Mathematics
- 2013

Quantization of compressed sensing measurements is typically justified by the robust recovery results of Candès, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size δ is used to quantize m measurements y = Φx of a k-sparse signal x ∈ R , where Φ satisfies the restricted isometry property, then the approximate… (More)

The compressed sensing problem for redundant dictionaries aims to use a small number of linear measurements to represent signals that are sparse with respect to a general dictionary. Under an appropriate restricted isometry property for a dictionary, reconstruction methods based on ` minimization are known to provide an effective signal recovery tool in… (More)

The second order Sigma-Delta (Σ∆) scheme with linear quantization rule is analyzed for quantizing finite unit-norm tight frame expansions for Rd. Approximation error estimates are derived, and it is shown that for certain choices of frames the quantization error is of order 1/N2, where N is the frame size. However, in contrast to the setting of bandlimited… (More)

The Balian–Low Theorem is a strong form of the uncertainty principle for Gabor systems which form orthonormal or Riesz bases for L(R). In this paper we investigate the Balian–Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian–Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several… (More)

- C. Sinan Güntürk, Alexander M. Powell, Rayan Saab, Özgür Yilmaz
- ArXiv
- 2010

Quantization of compressed sensing measurements is typically justified by the robust recovery results of Candès, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size δ is used to quantize m measurements y = Φx of a k-sparse signal x ∈ RN , where Φ satisfies the restricted isometry property, then the approximate… (More)

- John J. Benedetto, Alexander M. Powell, Hui-Chuan Wu
- ISBI
- 2002

- Alexander M. Powell, J. Tyler Whitehouse
- Foundations of Computational Mathematics
- 2016

Consistent reconstruction is a method for producing an estimate x̃ ∈ R of a signal x ∈ R if one is given a collection ofN noisy linear measurements qn = 〈x, φn〉+ǫn, 1 ≤ n ≤ N , that have been corrupted by i.i.d. uniform noise {ǫn}n=1. We prove mean squared error bounds for consistent reconstruction when the measurement vectors {φn}n=1 ⊂ R are drawn… (More)

- Mark Lammers, Alexander M. Powell, Özgür Yilmaz
- Adv. Comput. Math.
- 2010

We design alternative dual frames for linearly reconstructing signals from Sigma-Delta (Σ∆) quantized finite frame coefficients. In the setting of sampling expansions for bandlimited functions, it is known that a stable rth order Sigma-Delta quantizer produces approximations where the approximation error is at most of order 1/λ , and λ > 1 is the… (More)

- C. Sinan Güntürk, Mark Lammers, Alexander M. Powell, Rayan Saab, Özgür Yilmaz
- 2010 44th Annual Conference on Information…
- 2010

Recent results make it clear that the compressed sensing paradigm can be used effectively for dimension reduction. On the other hand, the literature on quantization of compressed sensing measurements is relatively sparse, and mainly focuses on pulse-code-modulation (PCM) type schemes where each measurement is quantized independently using a uniform… (More)