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- Özgür Yilmaz, Scott T. Rickard
- IEEE Transactions on Signal Processing
- 2004

Binary time-frequency masks are powerful tools for the separation of sources from a single mixture. Perfect demixing via binary time-frequency masks is possible provided the time-frequency representations of the sources do not overlap: a condition we call W-disjoint orthogonality. We introduce here the concept of approximate W-disjoint orthogonality and… (More)

- Alexander Jourjine, Scott T. Rickard, Özgür Yilmaz
- ICASSP
- 2000

We present a novel method for blind separation of any number of sources using only two mixtures. The method applies when sources are (W-)disjoint orthogonal, that is, when the supports of the (windowed) Fourier transform of any two signals in the mixture are disjoint sets. We show that, for anechoic mixtures of attenuated and delayed sources, the method… (More)

- Michael P. Friedlander, Hassan Mansour, Rayan Saab, Özgür Yilmaz
- IEEE Transactions on Information Theory
- 2012

We study recovery conditions of weighted <i>l</i><sub>1</sub> minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support information is accurate, then weighted <i>l</i><sub>1</sub> minimization is stable and robust under weaker sufficient… (More)

- Scott T. Rickard, Özgür Yilmaz
- 2002 IEEE International Conference on Acoustics…
- 2002

It is possible to blindly separate an arbitrary number of sources given just two anechoic mixtures provided the time-frequency representations of the sources do not overlap, a condition which we call W-disjoint orthogonality. We define a power weighted two-dimensional histogram constructed from the ratio of the time-frequency representations of the mixtures… (More)

- 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.

- Rayan Saab, Rick Chartrand, Özgür Yilmaz
- 2008 IEEE International Conference on Acoustics…
- 2008

We present theoretical results pertaining to the ability of lscr<sub>p</sub> minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Candes, Romberg and Tao (2005) to the p < 1 case. Our results indicate that depending on the restricted isometry constants (see, e.g., Candes… (More)

- 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)

- Rayan Saab, Özgür Yilmaz
- ArXiv
- 2008

In this note, we address the theoretical properties of ∆p, a class of compressed sensing decoders that rely on lp minimization with 0 < p < 1 to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. In particular, we extend the results of Candès, Romberg and Tao [4] and Wojtaszczyk [30] regarding the decoder ∆1,… (More)

- Hassan Mansour, Özgür Yilmaz
- ArXiv
- 2011

In this paper, we study the support recovery conditions of weighted `1 minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from `1 minimization provides an accurate support estimate. We then derive… (More)

- Özgür Yilmaz
- ArXiv
- 2014

We introduce a novel framework of reservoir computing. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a… (More)