DOA estimation in partially correlated noise using low-rank/sparse matrix decomposition

Malek-Mohammadi, Mohammadreza; Jansson, Magnus; Owrang, Arash; Koochakzadeh, Ali; Babaie‐Zadeh, Massoud

doi:10.1109/sam.2014.6882419

Cited by 12 publications

(12 citation statements)

References 14 publications

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“…This problem has many applications in various areas of engineering. For example, collaborative filtering [1], ultrasonic tomography [2], direction-of-arrival estimation [3], and machine learning [4] This work was supported in part by the Iran Telecommunication Research are some of these applications. For more comprehensive lists of applications, we refer the reader to [1], [5], [6].…”

Section: Introductionmentioning

confidence: 99%

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Iterative Concave Rank Approximation for Recovering Low-Rank Matrices

Malek-Mohammadi¹,

Babaie‐Zadeh²,

Skoglund³

2014

IEEE Trans. Signal Process.

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In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values, and then minimize the resulting approximation subject to the linear constraints. The accuracy of the approximation is controlled via a scaling parameter δ, where a smaller δ corresponds to a more accurate fitting. The consequent optimization problem for any finite δ is nonconvex. Therefore, to decrease the risk of ending up in local minima, a series of optimizations is performed, starting with optimizing a rough approximation (a large δ) and followed by successively optimizing finer approximations of the rank with smaller δ's. To solve the optimization problem for any δ > 0, it is converted to a new program in which the cost is a function of two auxiliary positive semidefinite variables. The paper shows that this new program is concave and applies a majorize-minimize technique to solve it which, in turn, leads to a few convex optimization iterations. This optimization scheme is also equivalent to a reweighted Nuclear Norm Minimization (NNM). For any δ > 0, we derive a necessary and sufficient condition for the exact recovery which are weaker than those corresponding to NNM. On the numerical side, the proposed algorithm is compared to NNM and a reweighted NNM in solving affine rank minimization and matrix completion problems showing its considerable and consistent superiority in terms of success rate.

QC 20150417

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Section: Introductionmentioning

confidence: 99%

“…Despite the convexity of the NNM program, there is a large gap between the sufficient conditions for the exact and robust recovery of low-rank matrices using (1) and (3) [18]. To narrow this gap, we introduce a novel algorithm based on successive and iterative minimization of a series of nonconvex replacements for (1).…”

Section: Introductionmentioning

confidence: 99%

Iterative Concave Rank Approximation for Recovering Low-Rank Matrices

Malek-Mohammadi¹,

Babaie‐Zadeh²,

Skoglund³

2014

IEEE Trans. Signal Process.

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QC 20150417

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“…In other words, (19) indicates that 1 is the lower bound on the smallest eigenvalue of generalized ED of R and Q. Thus, the noise subspace basis u l , l = 1, · · · , M − L is composed of M − L eigenvectors with the smallest eigenvalues.…”

Section: New Proposed Methodsmentioning

confidence: 99%

Non-Iterative Subspace-Based DOA Estimation in the Presence of Nonuniform Noise

Esfandiari

Vorobyov

Aliban

et al. 2019

IEEE Signal Process. Lett.

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The uniform white noise assumption is one of the basic assumptions in most of the existing directional-of-arrival (DOA) estimation methods. In many applications, however, the non-uniform white noise model is more adequate. Then the noise variances at different sensors have to be also estimated as nuisance parameters while estimating DOAs. In this letter, different from the existing iterative methods that address the problem of non-uniform noise, a non-iterative two-phase subspace-based DOA estimation method is proposed. The first phase of the method is based on estimating the noise subspace via eigendecomposition (ED) of some properly designed matrix and it avoids estimating the noise covariance matrix. In the second phase, the results achieved in the first phase are used to estimate the noise covariance matrix, followed by estimating the noise subspace via generalized ED. Since the proposed method estimates DOAs in a non-iterative manner, it is computationally more efficient and has no convergence issues as compared to the existing methods. Simulation results demonstrate better performance of the proposed method as compared to other existing state-of-the-art methods. Index TermsArray processing, direction-of-arrival (DOA) estimation, subspace based methods, nonuniform noise, spectral analysis.

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“…For this colored noise case, ROOT-MUSIC, SPECTRAL-MUSIC and SPICE are not directly applicable (they will give biased estimates). Instead, a numerical comparison is made with the newly pro posed method [16], we name it as mapped sr-LASSO (msr LASSO), is illustrated in Fig. 2 maps the support of the noise covariance matrix to zero.…”

Section: Scenario 2: Colored Noisementioning

confidence: 99%

Weighted covariance matching based square root LASSO

Owrang

Jansson

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose a method for high dimensional sparse estima tion in the multiple measurement vector case. The method is based on the covariance matching technique and with a sparse penalty along the ideas of the square-root LASSO (sr-LASSO). The method not only benefits from the strong characteristics of sr-LASSO (independence of the hyper parameter selection from the noise variance), but also offers a performance near maximum likelihood. It performs close to the Cramer-Rao bound even at low signal to noise ratios and it is generalized to manage correlated noise. The only assumption in this matter is that the noise covariance matrix structure is known. The numerical simulation provided in an array processing application illustrates the potential of the method.

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DOA estimation in partially correlated noise using low-rank/sparse matrix decomposition

Cited by 12 publications

References 14 publications

Iterative Concave Rank Approximation for Recovering Low-Rank Matrices

Iterative Concave Rank Approximation for Recovering Low-Rank Matrices

Non-Iterative Subspace-Based DOA Estimation in the Presence of Nonuniform Noise

Weighted covariance matching based square root LASSO

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