267 research outputs found

    Sparse approximations of protein structure from noisy random projections

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    Single-particle electron microscopy is a modern technique that biophysicists employ to learn the structure of proteins. It yields data that consist of noisy random projections of the protein structure in random directions, with the added complication that the projection angles cannot be observed. In order to reconstruct a three-dimensional model, the projection directions need to be estimated by use of an ad-hoc starting estimate of the unknown particle. In this paper we propose a methodology that does not rely on knowledge of the projection angles, to construct an objective data-dependent low-resolution approximation of the unknown structure that can serve as such a starting estimate. The approach assumes that the protein admits a suitable sparse representation, and employs discrete L1L^1-regularization (LASSO) as well as notions from shape theory to tackle the peculiar challenges involved in the associated inverse problem. We illustrate the approach by application to the reconstruction of an E. coli protein component called the Klenow fragment.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS479 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Interference Removal for Radar/Communication Co-existence: the Random Scattering Case

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    In this paper we consider an un-cooperative spectrum sharing scenario, wherein a radar system is to be overlaid to a pre-existing wireless communication system. Given the order of magnitude of the transmitted powers in play, we focus on the issue of interference mitigation at the communication receiver. We explicitly account for the reverberation produced by the (typically high-power) radar transmitter whose signal hits scattering centers (whether targets or clutter) producing interference onto the communication receiver, which is assumed to operate in an un-synchronized and un-coordinated scenario. We first show that receiver design amounts to solving a non-convex problem of joint interference removal and data demodulation: next, we introduce two algorithms, both exploiting sparsity of a proper representation of the interference and of the vector containing the errors of the data block. The first algorithm is basically a relaxed constrained Atomic Norm minimization, while the latter relies on a two-stage processing structure and is based on alternating minimization. The merits of these algorithms are demonstrated through extensive simulations: interestingly, the two-stage alternating minimization algorithm turns out to achieve satisfactory performance with moderate computational complexity
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