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Basis pursuit with sequential measurements and time varying signals

Basis pursuit with sequential measurements and time varying ...

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ieee international workshop on computational advances in multi-sensor adaptive processing (CAMSAP)

作者： M. Salman Asif Justin Romberg School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA USA

ISBN: (纸本)9781424451791;9781424451807

Recovery of sparse signals from linear measurements arises in several signal processing applications. Basis pursuit is a standard convex optimization program, often used to perform this task. In this paper we present two algorithms to dynamically update the solution of basis pursuit as (1) new measurements are sequentially added or (2) the underlying signal changes slightly. The goal is to avoid solving the (computationally expensive) optimization routine every time a small change occurs in the measurements. Our proposed update algorithms are based on homotopy principles, which iteratively update the solution by moving from an already solved problem towards the desired problem. Each homotopy step involves only a few matrix-vector multiplications. Simulation results show that the number of homotopy steps required for the update is comparable to the sparsity of the underlying signals.

关键词： Time measurement Signal processing Least squares methods Signal processing algorithms Electric variables measurement computational efficiency Image reconstruction Equations Conferences adaptive signal processing

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Fast sequential source localization using the Projected Companion Matrix approach

Fast sequential source localization using the Projected Comp...

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ieee international workshop on computational advances in multi-sensor adaptive processing (CAMSAP)

作者： Mohammed Nabil El Korso Remy Boyer Sylvie Marcos Laboratiore des Signaux et Systèmes (L2S) SUPELEC Université Paris-Sud XI (UPS) CNRS Gif-sur-Yvette France

ISBN: (纸本)9781424451791;9781424451807

The sequential forms of the spectral MUSIC algorithm, such as the sequential MUSIC (S-MUSIC) and the recursively applied and projected MUSIC (RAP-MUSIC) algorithms, use the previously estimated DOA (direction of arrival) to form an intermediate array gain matrix and project both the array manifold and the signal subspace estimate into its orthogonal complement. By doing this, these methods avoid the delicate search of multiple maxima and yield a more accurate DOA estimation in difficult scenarios. However, these high-resolution algorithms adapted to a general array geometry suffer from a high computational cost. On the other hand, for linear equispaced sensor array, the root-MUSIC algorithm is a fast and accurate high-resolution scheme which also avoids the delicate search of multiple maxima but a sequential scheme based on the root-MUSIC algorithm does not exist. This paper fills this need. Thus, we present a new sequential high-resolution estimation method, called the Projected Companion Matrix MUSIC (PCM-MUSIC) method, in the context of source localisation in the case of linear equispaced sensor array. Remark that the proposed algorithm can be used without modification in the context of spectral analysis.

关键词： sensor arrays Estimation error Direction of arrival estimation adaptive arrays Maximum likelihood estimation Statistics Energy consumption Costs Closed-form solution Degradation

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A sublinear algorithm for sparse reconstruction with ℓ2/ℓ2 recovery guarantees

A sublinear algorithm for sparse reconstruction with ℓ2/ℓ2...

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ieee international workshop on computational advances in multi-sensor adaptive processing (CAMSAP)

作者： Robert Calderbank Stephen Howard Sina Jafarpour Mathematics & Electrical Engineering Princeton University NJ USA DSTO Australia Edinburgh Australia Computer Science Princeton University NJ USA

Compressed sensing aims to capture attributes of a sparse signal using very few measurements. Candes and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all k-sparse signals. This property holds with overwhelming probability if the entries of the matrix are generated by an iid Gaussian or Bernoulli process. There has been significant recent interest in an alternative signal processing framework; exploiting deterministic sensing matrices that with overwhelming probability act as a near isometry on k-sparse vectors with uniformly random support, a geometric condition that is called the Statistical Restricted Isometry Property or StRIP. This paper considers a family of deterministic sensing matrices satisfying the StRIP that are based on Delsarte-Goethals Codes codes (binary chirps) and a k-sparse reconstruction algorithm with sublinear complexity. In the presence of stochastic noise in the data domain, this paper derives bounds on the l 2 accuracy of approximation in terms of the l 2 norm of the measurement noise and the accuracy of the best k-sparse approximation, also measured in the l 2 norm. This type of l 2 /l 2 bound is tighter than the standard l 2 /l 1 or l 1 /l 1 bounds.

关键词： Sparse matrices Strips Noise measurement Signal processing algorithms Compressed sensing Signal processing Probability Chirp Reconstruction algorithms Stochastic resonance

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Co-located MIMO radar with orthogonal waveform coding : Cramér-Rao Lower Bound

Co-located MIMO radar with orthogonal waveform coding : Cram...

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ieee international workshop on computational advances in multi-sensor adaptive processing (CAMSAP)

作者： Rémy Boyer Laboratiore des Signaux et Systèmes (L2S Université Paris-Sud XI CNRS SUPELEC Gif-sur-Yvette France

ISBN: (纸本)9781424451791;9781424451807

In this paper, we derive and analyze closed form (nonmatrix) expression of the Cramer-Rao lower bound (CRB) for the location and the velocity of moving targets contaminated by a structured noise (clutter echoes) and a background noise. The context of our analysis is the co-located MIMO (multiple-input multiple-output) radar system, ie., we dispose of multiple antennas in transmission and reception which are close in space. In addition as it is standard in modern MIMO radar, several noncoherent orthogonal waveforms are transmitted. The analysis of the proposed expressions of the CRB allows to better understand the characterisation of the target. In particular, we prove (1) the estimation of the direction parameter and the velocity of the target are cross-linked ; (2) it is more difficult to estimate the target velocity if the radar station is moving ; (3) if the radar station is not moving, the estimation of the target velocity is isotropic ; (4) it is more difficult to accurately localize fixed or slow moving targets and finally, the CRB for a MIMO radar is a lower bound of the one for the SIMO (single-input multiple-output) radar.

关键词： MIMO Radar antennas Background noise Clutter Spaceborne radar Transmitting antennas Receiving antennas Reflector antennas Stochastic processes Doppler radar

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Efficient and robust sensor data aggregation using linear counting sketches

Efficient and robust sensor data aggregation using linear co...

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10th workshop on advances in Parallel and Distributed computational Models/22nd ieee international Parallel and Distributed processing Symposium

作者： Fan, Yao-Chung Chen, Arbee L. P. Natl Tsing Hua Univ Dept Comp Sci Hsinchu 30043 Taiwan Natl Chengchi Univ Dept Comp Sci 64 Chihnan RdSec 2 Wenshan Taipei 11623 Taiwan

ISBN: (纸本)9781424416936

sensor networks have received considerable attention in recent years, and are often employed in the applications where data are difficult or expensive to collect. In these applications, in addition to individual sensor readings, statistical aggregates such as Min and Count over the readings of a group of sensor nodes are often needed. To conserve resources for sensor nodes, in-network strategies are adopted to process the aggregates. One primitive in-network aggregation strategy is the tree-based aggregation, where the aggregates are computed along a spanning tree over a sensor network. However, a shortcoming with the tree-based aggregation is that it is not robust against communication failures, which are common in sensor networks. One of the solutions to overcome this shortcoming is to enable multi-path routing, by which each node broadcasts its reading or a partial aggregate to multiple neighbors. However, multi-path routing based aggregation typically suffers from the problem of overcounting sensor readings. In this study, we propose using the linear counting sketches for multi-path routing based in-network aggregation. We claim that the use of the linear counting sketches makes our approach considerably more accurate than previous approaches using the same sketch space. Our approach also enjoys low variances in term of the aggregate accuracy, and low overheads either in computations or sketch space. Through extensive experiments with real-world and synthetic data, we demonstrate the efficiency and effectiveness of using the linear counting sketches as a solution for the innerwork aggregation.

关键词： Aggregates

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True Cramer-Rao bound for estimating synchronization parameters from a linearly modulated bandpass signal with unknown data symbols

True Cramer-Rao bound for estimating synchronization paramet...

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2nd ieee international workshop on computational advances in multi-sensor adaptive processing

作者： Noels, N. Moeneclaey, M. Univ Ghent DIGCOM Res Grp TELIN Dept B-9000 Ghent Belgium

ISBN: (纸本)9781424417131

This paper considers the Cramer-Rao bound (CRB) for estimating the synchronization parameters from a linearly modulated waveform with unknown data symbols. The key idea is to reduce the computational complexity associated with the CRB by exploiting the specific structure of the observed signal, see e.g., [1, 2] and references therein. The current contribution builds on this previous work, but in this case, no distributional assumptions are made about the data symbols. A generalized closed-form expression of the CRB is presented, the resulting computational complexity is discussed, and numerical results are provided.

关键词： Parameter estimation computational complexity Additive white noise Gaussian noise AWGN Closed-form solution Frequency synchronization Phase estimation Phase noise Phase modulation

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Robust autonomous detection of the faulty sensors of a sensor array

Robust autonomous detection of the faulty sensors of a senso...

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2nd ieee international workshop on computational advances in multi-sensor adaptive processing

作者： Ghosh, Siddhartha Freitas, Alex Marshall, Ian Univ Kent Comp Lab Canterbury CT2 7NF Kent England Univ Lancaster Ctr Environm Informat Lancaster LA1 4YW England

ISBN: (纸本)9781424417131

We propose a technique for the autonomous detection of the faulty sensors of a sensor array that are aberrant relative to the rest. Our approach is based on probabilistically modeling the distribution of the differences between the sensor measurements as a mixture of gaussians and then classifying further instances of the sensor differences using a naive bayes classifier. We demonstrate the applicability of this technique to the diagnosis of the sensors/photosites of a CCD array, using sensor array data comprising of randomly selected images. Our technique performs well for different combinations of parameter settings at the detection of the faulty photosites of a CCD array.

关键词： Charge coupled devices

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Analysis of the Cramer-Rao bound integrating a prior-knowledge

Analysis of the Cramer-Rao bound integrating a prior-knowled...

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2nd ieee international workshop on computational advances in multi-sensor adaptive processing

作者： Boyer, Remy Univ Paris 11 CNRS SUPELEC L2S Orsay France

ISBN: (纸本)9781424417131

Introducing prior-knowledge of some damped/undamped poles in the estimation of the parameters of a mutli-poles sinusoidal model is an important problem as for instance in bearing estimation or in biomedical signal analysis. The principle is to orthogonally project the data onto the noise space associated with the known poles. As the Cramer-Rao Lower Bound (CRB) gives a benchmark against which algorithms performance can be compared, it is useful to derive the CRB associated with this model, named Prior-CRB (P-CRB). In particular, we analyze this bound in the context of close subspaces context, ie., when the known poles are close to the unknown ones.

关键词： Benchmarking

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Robust multi-antenna broadcasting with imperfect channel state information

Robust multi-antenna broadcasting with imperfect channel sta...

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2nd ieee international workshop on computational advances in multi-sensor adaptive processing

作者： Wajid, Imran Gershman, Alex B. Vorobyov, Sergiy A. Karanouh, Yasser A. Tech Univ Darmstadt D-64283 Darmstadt Germany Univ Alberta Edmonton AB T6G 2M7 Canada

ISBN: (纸本)9781424417131

The problem of robust multi-antenna broadcasting is considered in the case of erroneous channel state information (CSI) at the transmitter. The criterion of minimum transmission power is used subject to the constraints guaranteeing that the signal-to-noise ratio (SNR) of each intended receiver satisfies a prescribed quality of service (QoS) requirement for the worst-case norm-bounded CSI mismatch. The resulting robust broadcasting problem is non-convex and, therefore, is difficult to solve. However, a suitable semi-definite relaxation (SDR) of this problem is proposed that enables to transform it to a convex form and to compute the optimal transmitter weight vector.

关键词： Broadcasting antennas

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Global DC optimization for multi-user interference systems

Global DC optimization for multi-user interference systems

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2nd ieee international workshop on computational advances in multi-sensor adaptive processing

作者： Xu, Yang Le-Ngoc, Tho McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 2A7 Canada

ISBN: (纸本)9781424417131

The weighted sum capacity of a Gaussian interference system is a nonconvex function of transmit power allocation vector of all users in the system. This paper shows that, by representing its objective function as a difference of two convex functions (d.c.), the non-convex optimization problem can be converted into an equivalent d.c. global optimization problem, which can be solved efficiently by various developed d.c. algorithms. In particular, a modified prismatic branch -and-bound algorithm that only requires solving a sequence of linear programming sub-problems, is introduced to find the global optimum. Simulation results in wireless flat-fading channel show that the proposed global d.c. optimization formulation outperforms considerably the local optimization methods in terms of achievable ergodic sum-rate capacity.

关键词： interference system weighted sum-rate capacity dc. optimization

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