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Identifiability in Bilinear Inverse Problems With Applications to Subspace or Sparsity-Constrained Blind Gain and Phase Calibration

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第2期63卷 822-842页

作者： Li, Yanjun Lee, Kiryung Bresler, Yoram Univ Illinois Dept Elect & Comp Engn Coordinated Sci Lab Champaign IL 61801 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, the properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the search space. These approaches have shown some success in practice. However, there are few results on uniqueness in BIPs. For most BIPs, the fundamental question of under what condition the problem admits a unique solution is yet to be answered. For example, blind gain and phase calibration (BGPC) is a structured BIP, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution (MBD). It is interesting to study the uniqueness of such problems. In this paper, we define identifiability of a BIP up to a group of transformations. We derive necessary and sufficient conditions for such identifiability, i.e., the conditions under which the solutions can be uniquely determined up to the transformation group. These conditions take the form of dividing the identifiability of the pair of unknown variables into the individual identifiability of each variable. Although verifying these individual conditions requires problem-specific procedures, this framework is universally applicable to all BIPs. Applying these results to BGPC, we derive sufficient conditions for unique recovery under several scenarios, including subspace, joint sparsity, and sparsity models. For BGPC with joint sparsity or sparsity constraints, we develop a procedure to compute the transformation groups corresponding to inherent ambiguities. We also give necessary conditions in the form of tight lower bounds on sample complexities, and demonstrate the tightness of these bounds by numerical experim

关键词： Ambiguity blind gain and phase calibration equivalence class inverse rendering multichannel blind deconvolution SAR autofocus sensor array processing transformation group uniqueness

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Compressive Sensing-based DOA Estimation using the Dantzig Selector 60

Compressive Sensing-based DOA Estimation using the Dantzig S...

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60th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)

作者： Salama, Amgad A. Ahmad, M. Omair Swamy, M. N. S. Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 1M8 Canada

ISBN: (纸本)9781509063895

In this paper, a new compressive sensing (CS)-based direction of arrival (DOA) estimation technique using the Dantzig selector is proposed. The proposed scheme can identify more source signals than the number of sensors used, without requiring an a priori knowledge of the number of source signals to be estimated and without any constraint or assumption about the nature of the signal sources using a fewer number of snapshots. The performance of the proposed scheme is compared to that of the Zhang penalty-based algorithm and the MVDR A-LASSO DOA estimation technique. The computational complexity of the proposed algorithm is substantially lower than that of the Zhang penalty-based method or MVDR A-LASSO.

关键词： Direction-of-arrival estimation sensor array processing Dantzig-selector Sparse array Compressive sensing

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Low Complexity Method for Wideband DOA Estimation Based on Sparse Representation Using Rotational Signal Subspace

Low Complexity Method for Wideband DOA Estimation Based on S...

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IEEE Radar Conference (RadarConf)

作者： Zhao, Yonghong Zhang, Linrang Zhang, Juan Guo, Yumei Gu, Yabin Xidian Univ Dept Elect Engn Natl Lab Radar Signal Proc Xian 710071 Shaanxi Peoples R China

ISBN: (纸本)9781467388238

A low complexity method for wideband direction finding based on sparse representation is proposed, which combines the rotational signal subspace (RSS) with weighted subspace fitting (WSF) to improve the performance of DOA estimation. Exploiting the result of the focusing operation, the covariance matrix at the focusing frequency can be obtained and used as the data for sparse recovery to get wideband DOA estimates. The WSF is employed to reduce the sensitivity to the noise and the regularization parameter is given by the asymptotic distribution of the WSF criterion. Simulations are provided to prove the efficiency and performance of the proposed method.

关键词： direction-of-arrival (DOA) estimation sparse representation sensor array processing

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Subspace-based interference removal methods for a multichannel biomagnetic sensor array

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JOURNAL OF NEURAL ENGINEERING 2017年第5期14卷 051001-051001页

作者： Sekihara, Kensuke Nagarajan, Srikantan S. Signal Anal Inc Hachioji Tokyo Japan Tokyo Med & Dent Univ Dept Adv Technol Med Bunkyo Ku 1-5-45 Yushima Tokyo 1138519 Japan Univ Calif San Francisco Biomagnet Imaging Lab 513 Parnassus AveS362 San Francisco CA 94143 USA

Objective. In biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in which the signal/interference subspace is defined in the spatial domain as the span of signal/interference-source lead field vectors. This paper extends the notion of this conventional (spatial domain) signal subspace by introducing a new definition of signal subspace in the time domain. Approach. It defines the time-domain signal subspace as the span of row vectors that contain the source time course values. This definition leads to symmetric relationships between the time-domain and the conventional (spatial-domain) signal subspaces. As a review, this article shows that the notion of the time-domain signal subspace provides useful insights over existing interference removal methods from a unified perspective. Main results and significance. Using the time-domain signal subspace, it is possible to interpret a number of interference removal methods as the time domain signal space projection. Such methods include adaptive noise canceling, sensor noise suppression, the common temporal subspace projection, the spatio-temporal signal space separation, and the recently-proposed dual signal subspace projection. Our analysis using the notion of the time domain signal space projection reveals implicit assumptions these methods rely on, and shows that the difference between these methods results only from the manner of deriving the interference subspace. Numerical examples that illustrate the results of our arguments are provided.

关键词： interference removal magnetoencephalography sensor array processing signal subspace biomagnetic imaging biomagnetism multi-sensor array

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Optimal Sample Complexity for Blind Gain and Phase Calibration

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IEEE TRANSACTIONS ON SIGNAL processing 2016年第21期64卷 5549-5556页

作者： Li, Yanjun Lee, Kiryung Bresler, Yoram Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

Blind gain and phase calibration (BGPC) is a structured bilinear inverse problem, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution. The fundamental question of the uniqueness of the solutions to such problems has been addressed only recently. In a previous paper, we proposed studying the identifiability in bilinear inverse problems up to transformation groups. In particular, we studied several special cases of blind gain and phase calibration, including the cases of subspace and joint sparsity models on the signals, and gave sufficient and necessary conditions for identifiability up to certain transformation groups. However, there were gaps between the sample complexities in the sufficient conditions and the necessary conditions. In this paper, under a mild assumption that the signals and models are generic, we bridge the gaps by deriving tight sufficient conditions with optimal or near optimal sample complexities.

关键词： Blind gain and phase calibration inverse rendering multichannel blind deconvolution SAR autofocus sensor array processing

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New Approaches to Direction-of-Arrival Estimation With sensor arrays in Unknown Nonuniform Noise

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IEEE sensorS JOURNAL 2016年第24期16卷 8982-8989页

作者： Liao, Bin Huang, Lei Guo, Chongtao So, Hing Cheung Shenzhen Univ Coll Informat Engn Shenzhen 518060 Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China

It is known that classical subspace-based direction-of-arrival (DOA) estimation algorithms are not straightforwardly applicable to scenarios with unknown spatially nonuniform noise. Among the state-of-the-art solutions, this problem is tackled by iterative subspace estimation algorithms to incorporate subspace-based approaches or nonlinear optimization routines to bypass the direct identification of subspaces. In this paper, the problem of DOA estimation in nonuniform noise is revisited by devising two computationally efficient proposals. It is proved herein that, if the signals are uncorrelated, the signal and noise subspaces can be directly obtained from the eigendecomposition of a reduced array covariance matrix. On the other hand, when the signals are correlated, the estimation of the noise covariance matrix is formulated into a rank minimization problem which can be approximately solved by semidefinite programming. In both cases, the signal and noise subspaces are easy to compute without iterations. Consequently, classical subspace-based algorithms can be employed to determine the DOAs. Numerical examples are provided to demonstrate the performance and applicability of the proposed methods.

关键词： sensor array processing direction-of-arrival estimation nonuniform noise semidefinite programming

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Implementation Aspects of Joint Angle and Delay Estimation for Road Traffic Applications 6

Implementation Aspects of Joint Angle and Delay Estimation f...

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IEEE 6th International Conference on Communications and Electronics (IEEE ICCE)

作者： Patelczyk, Timo Biebl, Erwin Tech Univ Munich Fachgebiet Hochstfrequenztech Arcisstr 21 D-80333 Munich Germany

ISBN: (纸本)9781509018017

This paper provides an overview of implementation aspects of an algorithm for joint angle and delay estimation using shift-invariance techniques (SI-JADE) based on theoretical considerations. Objective is an assessment of computational complexity in terms of a real-time capable system design. This is an important step towards a practical implementation on an available hardware platform. The focus is on a time critical application for protection of vulnerable road users. A position determination of these, relative to a localization vehicle, allows an assistance of the driver in case of critical situations. For this purpose a field programmable gate array (FPGA) will be assumed as a platform. At this point two implementation aspects are discussed. The first one is a runtime optimized implementation of such a localization algorithm. The second aspect is that hardware resources can not be neglected. This is strongly linked to a practical implementation. In addition, theoretical results of computational complexity will be transferred to the application. At this point the urban and rural environment will be considered. These scenarios represent the worst case in terms of an implementation for the application. The objective is to show limitations of an implementation. Finally, a reduction of computational complexity is presented. This will allow a real-time capable implementation.

关键词： joint angle and delay estimation multiray propagation sensor array processing FPGA implementation

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MAXIMUM LIKELIHOOD AND MAXIMUM A POSTERIORI DIRECTION-OF-ARRIVAL ESTIMATION IN THE PRESENCE OF SIRP NOISE 41

MAXIMUM LIKELIHOOD AND MAXIMUM A POSTERIORI DIRECTION-OF-ARR...

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41st IEEE International Conference on Acoustics, Speech and Signal processing (ICASSP)

作者： Zhang, Xin El Korso, Mohammed Nabil Pesavento, Marius Tech Univ Darmstadt Commun Syst Grp Darmstadt Germany Univ Paris Ouest Nanterre La Def LEME EA416 Ville Davray France

ISBN: (纸本)9781479999880

The maximum likelihood (ML) and maximum a posteriori (MAP) estimation techniques are widely used to address the direction-of-arrival (DOA) estimation problems, an important topic in sensor array processing. Conventionally the ML estimators in the DOA estimation context assume the sensor noise to follow a Gaussian distribution. In real-life application, however, this assumption is sometimes not valid, and it is often more accurate to model the noise as a non-Gaussian process. In this paper we derive an iterative ML as well as an iterative MAP estimation algorithm for the DOA estimation problem under the spherically invariant random process noise assumption, one of the most popular non-Gaussian models, especially in the radar context. Numerical simulation results are provided to assess our proposed algorithms and to show their advantage in terms of performance over the conventional ML algorithm.

关键词： Direction-of-arrival estimation spherically invariant random process maximum likelihood estimation maximum a posteriori estimation sensor array processing

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Compressive Sensing-based DOA Estimation using the Dantzig Selector

Compressive Sensing-based DOA Estimation using the Dantzig S...

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IEEE Pulsed Power Conference

作者： Amgad A. Salama M. Omair Ahmad M. N. S. Swamy Department of Electrical and Computer Engineering Concordia University

ISBN: (纸本)9781509063901

关键词： Direction-of-arrival estimation sensor array processing Dantzig-selector Sparse array Compressive sensing

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Underdetermined DOA Estimation Using MVDR-Weighted LASSO

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sensorS 2016年第9期16卷 1549-1549页

作者： Salama, Amgad A. Ahmad, M. Omair Swamy, M. N. S. Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 1M8 Canada

The direction of arrival (DOA) estimation problem is formulated in a compressive sensing (CS) framework, and an extended array aperture is presented to increase the number of degrees of freedom of the array. The ordinary least square adaptable least absolute shrinkage and selection operator (OLS A-LASSO) is applied for the first time for DOA estimation. Furthermore, a new LASSO algorithm, the minimum variance distortionless response (MVDR) A-LASSO, which solves the DOA problem in the CS framework, is presented. The proposed algorithm does not depend on the singular value decomposition nor on the orthogonality of the signal and the noise subspaces. Hence, the DOA estimation can be done without a priori knowledge of the number of sources. The proposed algorithm can estimate up to ((M2 2) /2 + M 1) /2 sources using M sensors without any constraints or assumptions about the nature of the signal sources. Furthermore, the proposed algorithm exhibits performance that is superior compared to that of the classical DOA estimation methods, especially for low signal to noise ratios (SNR), spatially-closed sources and coherent scenarios.

关键词： adaptable LASSO sparse array direction of arrival estimation compressive sensing sensor array processing

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