42,596 research outputs found

    On the role of total variation in compressed sensing

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    This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with noise. We prove that in order to obtain a reconstruction which is robust to noise and stable to inexact gradient sparsity of order ss with high probability, it suffices to draw O(slogN)\mathcal{O}(s \log N) of the available Fourier coefficients uniformly at random. However, we also show that if one draws O(slogN)\mathcal{O}(s \log N) samples in accordance to a particular distribution which concentrates on the low Fourier frequencies, then the stability bounds which can be guaranteed are optimal up to log\log factors. Finally, we prove that in the one dimensional case where the underlying signal is gradient sparse and its sparsity pattern satisfies a minimum separation condition, then to guarantee exact recovery with high probability, for some M<NM<N, it suffices to draw O(slogMlogs)\mathcal{O}(s\log M\log s) samples uniformly at random from the Fourier coefficients whose frequencies are no greater than MM

    Solving the Solar Neutrino Problem 2 km Underground -- the Sudbury Neutrino Observatory

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    The Sudbury Neutrino Observatory (SNO) is capable of measuring simultaneously the flux of electron-type neutrinos and the total flux of all active flavours of neutrinos originating from the Sun. A model-independent test of neutrino flavour transformation was performed by comparing these two measurements. Assuming an undistorted neutrino energy spectrum, this transformation has been definitively demonstrated in the pure D2O phase of the SNO experiment. In the second phase with dissolved NaCl in the D2O, the total active solar neutrino flux was measured without any assumption on the energy dependence of flavour transformation. In this talk, results from these measurements, their physics implications and the current status of the SNO experiment are presented.Comment: Proceedings of the 8th ICATPP Conference on Astroparticle, Particle, Space Physics, Detectors and Medical Physics Applications (Como, Italy, Oct 6-10, 2003) 10 pages, 3 figures, 2 table
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