Non-uniform spatial sampling geometries, such as nested and coprime arrays, are provably capable of localizing O (M-2) sources using only M sensors. However, such guarantees require the physical locations of the senso...
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Non-uniform spatial sampling geometries, such as nested and coprime arrays, are provably capable of localizing O (M-2) sources using only M sensors. However, such guarantees require the physical locations of the sensors to satisfy certain constraints, as dictated by the corresponding array geometries. In this paper, we consider the scenario when these constraints may be violated, leading to unknown perturbations on the locations of sensors. Such perturbations can have detrimental effect on the performance of virtual array based direction-of-arrival (DOA) estimation algorithms, since the perturbed virtual array will no longer be a uniform linear array (ULA). We propose a novel self-calibration approach for underdetermined DOA estimation with such arrays, that makes extensive use of the redundancies (or repeated elements) in the virtual array. Assuming small perturbations, and a sparse grid-based model for the DOAs, we extract a novel "bi-affine" model (affine in the perturbation variable, and linear in the source powers) from the covariance matrix of the received signals. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers, from which the DOAs can be exactly recovered under suitable conditions. This reduction is derived for both ULA and a newly introduced robust version of coprime arrays, when the covariance matrix of the received signals is exactly known. Our approach is compared and contrasted with recently developed algorithms for blind gain and phase calibration (BGPC), whose signal model is fundamentally different from ours. We also provide an iterative algorithm to jointly solve for the DOAs and perturbation values when we can only estimate the covariance matrix using a finite number of snapshots. (C) 2016 Elsevier Inc. All rights reserved.
Objective: Cortical source imaging aims at identifying activated cortical areas on the surface of the cortex from the raw electroencephalogram (EEG) data. This problem is ill posed, the number of channels being very l...
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Objective: Cortical source imaging aims at identifying activated cortical areas on the surface of the cortex from the raw electroencephalogram (EEG) data. This problem is ill posed, the number of channels being very low compared to the number of possible source positions. Methods: In some realistic physiological situations, the active areas are sparse in space and of short time durations, and the amount of spatio-temporal data to carry the inversion is then limited. In this study, we propose an original data driven space-time-frequency (STF) dictionary which takes into account simultaneously both spatial and time-frequency sparseness while preserving smoothness in the time frequency (i.e., nonstationary smooth time courses in sparse locations). Based on these assumptions, we take benefit of the matching pursuit (MP) framework for selecting the most relevant atoms in this highly redundant dictionary. Results: We apply two recent MP algorithms, single best replacement (SBR) and source deflated matching pursuit, and we compare the results using a spatial dictionary and the proposed STF dictionary to demonstrate the improvements of our multidimensional approach. We also provide comparison using well-established inversion methods, FOCUSS and RAP-MUSIC, analyzing performances under different degrees of nonstationarity and signal to noise ratio. Conclusion: Our STF dictionary combined with the SBR approach provides robust performances on realistic simulations. Froma computational point of view, the algorithm is embedded in the wavelet domain, ensuring high efficiency in term of computation time. Significance: The proposed approach ensures fast and accurate sparse cortical localizations on highly nonstationary and noisy data.
Local Field Potential (LFP) recordings are one type of intracortical recordings, (besides Single Unit Activity) that can help decode movement direction successfully. In the long-term however, using LFPs for decoding p...
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ISBN:
(纸本)9781457702167
Local Field Potential (LFP) recordings are one type of intracortical recordings, (besides Single Unit Activity) that can help decode movement direction successfully. In the long-term however, using LFPs for decoding presents some major challenges like inherent instability and non-stationarity. Our approach to overcome this challenge bases around the hypothesis that each task has a signature source-location pattern. The methodology involves introduction of sourcelocalization, and tracking of sources over a period of time that enables us to decode movement direction in an eight-direction center-out-reach-task. We establish that such tracking can be used for long term decoding, with preliminary results indicating consistent patterns. In fact, tracking task related source locations render up to 66% accuracy in decoding movement direction one week after the decoding model was learnt.
We suggest a branch and bound algorithm for solving continuous optimization problems where a (generally nonconvex) objective function is to be minimized under nonconvex inequality constraints which satisfy some specif...
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We suggest a branch and bound algorithm for solving continuous optimization problems where a (generally nonconvex) objective function is to be minimized under nonconvex inequality constraints which satisfy some specific solvability assumptions. The assumptions hold for some special cases of nonconvex quadratic optimization problems. We show how the algorithm can be applied to the problem of minimizing a nonconvex quadratic function under ball, out-of-ball and linear constraints. The main tool we utilize is the ability to solve in polynomial computation time the minimization of a general quadratic under one Euclidean sphere constraint, namely the so-called trust region subproblem, including the computation of all local minimizers of that problem. Application of the algorithm on sparse source localization problems is presented.
Local Field Potential (LFP) recordings are one type of intra-cortical recordings, (besides Single Unit Activity) that can help decode movement direction successfully. In the long-term however, using LFPs for decoding ...
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ISBN:
(纸本)9781457702150
Local Field Potential (LFP) recordings are one type of intra-cortical recordings, (besides Single Unit Activity) that can help decode movement direction successfully. In the long-term however, using LFPs for decoding presents some major challenges like inherent instability and non-stationarity. Our approach to overcome this challenge bases around the hypothesis that each task has a signature source-location pattern. The methodology involves introduction of sourcelocalization, and tracking of sources over a period of time that enables us to decode movement direction in an eight-direction center-out-reach-task. We establish that such tracking can be used for long term decoding, with preliminary results indicating consistent patterns. In fact, tracking task related source locations render up to 66% accuracy in decoding movement direction one week after the decoding model was learnt.
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