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—Binary time-frequency masks are a powerful tool for the separation of sources from a single mixture. Perfect demix-ing 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)

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)

In this paper we study recovery conditions of weighted ℓ 1 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 ℓ 1 minimization is stable and robust under weaker conditions than the analogous… (More)

We present theoretical results pertaining to the ability of ℓp minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Candès, Romberg and Tao [1] to the p < 1 case. Our results indicate that depending on the restricted isometry constants (see, e.g., [2] and [3]) and the noise… (More)

—The-level Sigma–Delta (61) scheme with step size is introduced as a technique for quantizing finite frame expansions for. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that 61 quantization of a unit-norm finite frame expansion in achieves approximation error 2 (() + 1) where is the frame size, and the… (More)

This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with β = φ = (1 + √ 5)/2, the golden ratio. It was previously shown that beta-encoders can be implemented in… (More)

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)

In this note, we address the theoretical properties of ∆p, a class of compressed sensing decoders that rely on ℓ p minimization with p ∈ (0, 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 [3] and Wojtaszczyk [30] regarding the decoder ∆ 1… (More)

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 N , where Φ satisfies the restricted isometry property, then the approximate… (More)

The Kaczmarz algorithm is a popular solver for overdeter-mined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear equations with sparse solutions. The speedup is achieved by projecting every iterate onto a weighted row of the… (More)