scholarly journals Putting the Squeeze on Array Programs: Loop Verification via Inductive Rank Reduction

2020 ◽  
pp. 112-135 ◽  
Author(s):  
Oren Ish-Shalom ◽  
Shachar Itzhaky ◽  
Noam Rinetzky ◽  
Sharon Shoham
Keyword(s):  
Rank Reduction

scholarly journals Efficient Localization Algorithm for Near-Field Noncircular Sources via Dual-Polarization Sensor Array

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Jiaqi Song ◽  
Haihong Tao
Keyword(s):  
Source Localization ◽  
Near Field ◽  
Nuisance Parameter ◽  
Estimation Accuracy ◽  
Localization Algorithm ◽  
Dual Polarization ◽  
Rank Reduction ◽  
Localization Accuracy ◽  
Noncircular Signals ◽  
Polarization Sensor

Noncircular signals are widely used in the area of radar, sonar, and wireless communication array systems, which can offer more accurate estimates and detect more sources. In this paper, the noncircular signals are employed to improve source localization accuracy and identifiability. Firstly, an extended real-valued covariance matrix is constructed to transform complex-valued computation into real-valued computation. Based on the property of noncircular signals and symmetric uniform linear array (SULA) which consist of dual-polarization sensors, the array steering vectors can be separated into the source position parameters and the nuisance parameter. Therefore, the rank reduction (RARE) estimators are adopted to estimate the source localization parameters in sequence. By utilizing polarization information of sources and real-valued computation, the maximum number of resolvable sources, estimation accuracy, and resolution can be improved. Numerical simulations demonstrate that the proposed method outperforms the existing methods in both resolution and estimation accuracy.

scholarly journals Efficient Two-Dimensional Direction Finding Algorithm for Rectilinear Sources Under Unknown Mutual Coupling

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1914
Author(s):  
Jian Xie ◽  
Qiuping Wang ◽  
Yuexian Wang ◽  
Xin Yang
Keyword(s):  
Degrees Of Freedom ◽  
Mutual Coupling ◽  
Array Signal Processing ◽  
Elevation Angle ◽  
Doa Estimation ◽  
Two Dimensional ◽  
Rank Reduction ◽  
Communication Signals ◽  
Estimation Performance ◽  
Direction Cosines

Digital communication signals in wireless systems may possess noncircularity, which can be used to enhance the degrees of freedom for direction-of-arrival (DOA) estimation in sensor array signal processing. On the other hand, the electromagnetic characteristics between sensors in uniform rectangular arrays (URAs), such as mutual coupling, may significantly deteriorate the estimation performance. To deal with this problem, a robust real-valued estimator for rectilinear sources was developed to alleviate unknown mutual coupling in URAs. An augmented covariance matrix was built up by extracting the real and imaginary parts of observations containing the circularity and noncircularity of signals. Then, the actual steering vector considering mutual coupling was reparameterized to make the rank reduction (RARE) property available. To reduce the computational complexity of two-dimensional (2D) spectral search, we individually estimated y-axis and x-axis direction-cosines in two stages following the principle of RARE. Finally, azimuth and elevation angle estimates were determined from the corresponding direction-cosines respectively. Compared with existing solutions, the proposed method is more computationally efficient, involving real-valued operations and decoupled 2D spectral searches into twice those of one-dimensional searches. Simulation results verified that the proposed method provides satisfactory estimation performance that is robust to unknown mutual coupling and close to the counterparts based on 2D spectral searches, but at the cost of much fewer calculations.

Nonnegative rank factorization—a heuristic approach via rank reduction

2013 ◽  
Vol 65 (2) ◽  
pp. 251-274 ◽  
Author(s):  
Bo Dong ◽  
Matthew M. Lin ◽  
Moody T. Chu
Keyword(s):  
Heuristic Approach ◽  
Rank Reduction ◽  
Nonnegative Rank ◽  
Rank Factorization

scholarly journals Extended rank reduction formulas containing Wedderburn and Abaffy–Broyden–Spedicato rank reducing processes

2013 ◽  
Vol 439 (11) ◽  
pp. 3318-3331 ◽  
Author(s):  
Nezam Mahdavi-Amiri ◽  
Effat Golpar-Raboky
Keyword(s):  
Rank Reduction

Enhanced low-rank matrix estimation for simultaneous denoising and reconstruction of five-dimensional seismic data

Geophysics ◽  
2021 ◽  
pp. 1-96
Author(s):  
Yapo Abolé Serge Innocent Oboué ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Hankel Matrix ◽  
Low Rank ◽  
The Novel ◽  
Proximity Function ◽  
Rank Reduction ◽  
Matrix Estimation ◽  
Useful Signal ◽  
Truncated Svd ◽  
Noisy Observation

Noise and missing traces usually influence the quality of multidimensional seismic data. It is, therefore, necessary to e stimate the useful signal from its noisy observation. The damped rank-reduction (DRR) method has emerged as an effective method to reconstruct the useful signal matrix from its noisy observation. However, the higher the noise level and the ratio of missing traces, the weaker the DRR operator becomes. Consequently, the estimated low-rank signal matrix includes a unignorable amount of residual noise that influences the next processing steps. This paper focuses on the problem of estimating a low-rank signal matrix from its noisy observation. To elaborate on the novel algorithm, we formulate an improved proximity function by mixing the moving-average filter and the arctangent penalty function. We first apply the proximity function to the level-4 block Hankel matrix before the singular value decomposition (SVD), and then, to singular values, during the damped truncated SVD process. The relationship between the novel proximity function and the DRR framework leads to an optimization problem, which results in better recovery performance. The proposed algorithm aims at producing an enhanced rank-reduction operator to estimate the useful signal matrix with a higher quality. Experiments are conducted on synthetic and real 5-D seismic data to compare the effectiveness of our approach to the DRR approach. The proposed approach is shown to obtain better performance since the estimated low-rank signal matrix is cleaner and contains less amount of artifacts compared to the DRR algorithm.

Record-length Extension by Rank-reduction De-blending

2016 ◽  
Author(s):  
M. Maraschini ◽  
A. Kielius ◽  
J.B. Barnes ◽  
S. Grion
Keyword(s):  
Rank Reduction ◽  
Record Length
Sign in / Sign up

Export Citation Format

Share Document