Covariance Matching Estimation Techniques for Array Signal Processing Applications

Ottersten, Björn; Stoica, Petre; Roy, R.

doi:10.1006/dspr.1998.0316

Cited by 366 publications

(278 citation statements)

References 66 publications

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“…, where ⊗ denotes the Kronecker product), the weighted LS estimate is asymptotically equivalent to the maximum likelihood estimate [9]. It is straightforward to extend this vectorized formulation to include multiple snapshots over time and frequency to improve the imaging result [8].…”

Section: Problem Statementmentioning

confidence: 99%

Data driven model based least squares image reconstruction for radio astronomy

Wijnholds

Veen

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Image reconstruction problems in radio astronomy and other fields like biomedical imaging are often ill-posed and some form of regularization is required. This imposes user specified constraints to the reconstruction process that may produce an undesirable bias to the solution. We propose a data driven model based least squares reconstruction method based on the Karhunen-Loève transform. We show that this constraint stems from intrinsic physical properties of the measurement process and demonstrate the improvement of the method over unregularized least squares reconstruction using actual data from the Low Frequency Array (LOFAR), a phased array radio telescope in the Netherlands.

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Section: Problem Statementmentioning

confidence: 99%

Data driven model based least squares image reconstruction for radio astronomy

Wijnholds

Veen

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…We choose the individual sparsity regularization parameter as the one that is optimal for the infinite number of obtained snapshots. This parameter choice allows us to reformulate the problem as a purely group Lasso problem and make a connection to the Covariance Matching Estimation Technique (COMET) framework from [20] to determine the second regularization parameter for the group sparsity, based on the noise in the system. We compare the performance of the system with conventional methods for wideband direction of arrival estimation.…”

Section: This Paper Is a Revised And Expanded Version Of The Paper Prmentioning

confidence: 99%

Sparse covariance fitting method for direction of arrival estimation of uncorrelated wideband signals

Pejoski¹,

Kafedziski²

2014

Telfor

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“…Consider the problem of estimating the covariance matrix Σ of a random vector x with components x[n] when it is known that Σ is a linear combination of the matrices in the set S. This problem has a long history and a wide range of applications [1], [2]. Now consider a modification of the same problem where only a subset of the samples x[n] is available, i.e., when the observations are y[m] = x[n m ] for some I = {n 0 , n 1 , .…”

Section: Problem Statementmentioning

confidence: 99%

Compressive covariance sampling

Romero

Leus

2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-Most research efforts in the field of compressed sensing have been pointed towards analyzing sampling and reconstruction techniques for sparse signals, where sampling rates below the Nyquist rate can be reached. When only second-order statistics or, equivalently, covariance information is of interest, perfect signal reconstruction is not required and rate reductions can be achieved even for non-sparse signals. This is what we will refer to as compressive covariance sampling. In this paper, we will study minimum-rate compressive covariance sampling designs within the class of non-uniform samplers. Necessary and sufficient conditions for perfect covariance reconstruction will be provided and connections to the well-known sparse ruler problem will be highlighted. I. PROBLEM STATEMENTConsider the problem of estimating the covariance matrix Σ of a random vector x with components x[n] when it is known that Σ is a linear combination of the matrices in the set S. This problem has a long history and a wide range of applications [1], [2]. Now consider a modification of the same problem where only a subset of the samples x[n] is available, i.e., when the observations are y[m] = x[n m ] for some I = {n 0 , n 1 , . . .} ⊂ Z. Intuitively, if the grid defined by I is dense enough, then this estimation problem, which we label as compressive covariance sampling, can still be solved.More specifically, the above sample selection produces a transformation of the problem: the vector y collecting the compressed observations y[m], has a covariance matrixΣ, which is a linear combination of the matrices inS. The coefficients in the linear combination are in both problems the same so that solving the latter amounts to solving the former. In this paper we address the optimal design of the index set I so that the coefficients can be estimated, i.e., we look for sets of indices with a minimum number of elements guaranteeing that these parameters remain statistically identifiable. A. Relation to Compressive SamplingRecent interest in sampling signals below their Nyquist rate owes to compressive sampling (or compressed sensing) [3], which has motivated a great deal of research efforts in the last few years. In compressive sampling we are interested in reducing the number of samples by focusing on a special family of signals referred to as sparse. These signals are intrinsically redundant, so that this reduction does not entail any information loss if properly done.Non-uniform sampling [4] is a particular case of compressive sampling. Mathematically, this process can be described as first acquiring a continuous-index signal x(t) at rate 1/T , resulting in the sequence x[n] = x(nT ), and then downsampling x[n] to obtain y[m] according to a set of indices I, in a periodic or non-periodic fashion (periodic non-uniform sampling is also known as multi-coset sampling).Either in the context of compressive sampling (the nonuniform sampling version) or in the context of what we call compressive covariance sampling, the design of the set I has ...

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Covariance Matching Estimation Techniques for Array Signal Processing Applications

Cited by 366 publications

References 66 publications

Data driven model based least squares image reconstruction for radio astronomy

Data driven model based least squares image reconstruction for radio astronomy

Sparse covariance fitting method for direction of arrival estimation of uncorrelated wideband signals

Compressive covariance sampling

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