scholarly journals Identification of Linear and Bilinear Systems: A Unified Study

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1790
Author(s):  
Jacob Benesty ◽  
Constantin Paleologu ◽  
Laura-Maria Dogariu ◽  
Silviu Ciochină
Keyword(s):  
System Identification ◽  
Wiener Filter ◽  
Low Rank ◽  
Identification Problems ◽  
Low Rank Approximation ◽  
Product Decomposition ◽  
Single Output ◽  
Unified Study ◽  
Recent Developments ◽  
Improved Performance

System identification problems are always challenging to address in applications that involve long impulse responses, especially in the framework of multichannel systems. In this context, the main goal of this review paper is to promote some recent developments that exploit decomposition-based approaches to multiple-input/single-output (MISO) system identification problems, which can be efficiently solved as combinations of low-dimension solutions. The basic idea is to reformulate such a high-dimension problem in the framework of bilinear forms, and to then take advantage of the Kronecker product decomposition and low-rank approximation of the spatiotemporal impulse response of the system. The validity of this approach is addressed in terms of the celebrated Wiener filter, by developing an iterative version with improved performance features (related to the accuracy and robustness of the solution). Simulation results support the main theoretical findings and indicate the appealing performance of these developments.

scholarly journals Regularized Auto-Encoder-Based Separation of Defects from Backgrounds for Inspecting Display Devices

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 533 ◽  
Author(s):  
Heeyeon Jo ◽  
Jeongtae Kim
Keyword(s):  
Experimental Studies ◽  
Low Rank ◽  
Reconstruction Method ◽  
Low Rank Approximation ◽  
Display Devices ◽  
Singular Value Decomposition Method ◽  
Novel Method ◽  
Rank Approximation ◽  
Improved Performance ◽  
Value Decomposition

We investigated a novel method for separating defects from the background for inspecting display devices. Separation of defects has important applications such as determining whether the detected defects are truly defective and the quantification of the degree of defectiveness. Although many studies on estimating patterned background have been conducted, the existing studies are mainly based on the approach of approximation by low-rank matrices. Because the conventional methods face problems such as imperfect reconstruction and difficulty of selecting the bases for low-rank approximation, we have studied a deep-learning-based foreground reconstruction method that is based on the auto-encoder structure with a regression layer for the output. In the experimental studies carried out using mobile display panels, the proposed method showed significantly improved performance compared to the existing singular value decomposition method. We believe that the proposed method could be useful not only for inspecting display devices but also for many applications that involve the detection of defects in the presence of a textured background.

scholarly journals System Identification Based on Tensor Decompositions: A Trilinear Approach

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 556 ◽  
Author(s):  
Laura-Maria Dogariu ◽  
Silviu Ciochină ◽  
Jacob Benesty ◽  
Constantin Paleologu
Keyword(s):  
System Identification ◽  
Nonlinear Systems ◽  
Wiener Filter ◽  
Nonlinear Behavior ◽  
Hammerstein Model ◽  
Least Mean Square ◽  
Tensor Decompositions ◽  
Single Output ◽  
Long Time ◽  
Spatiotemporal Models

The theory of nonlinear systems can currently be encountered in many important fields, while the nonlinear behavior of electronic systems and devices has been studied for a long time. However, a global approach for dealing with nonlinear systems does not exist and the methods to address this problem differ depending on the application and on the types of nonlinearities. An interesting category of nonlinear systems is one that can be regarded as an ensemble of (approximately) linear systems. Some popular examples in this context are nonlinear electronic devices (such as acoustic echo cancellers, which are used in applications for two-party or multi-party voice communications, e.g., videoconferencing), which can be modeled as a cascade of linear and nonlinear systems, similar to the Hammerstein model. Multiple-input/single-output (MISO) systems can also be regarded as separable multilinear systems and be treated using the appropriate methods. The high dimension of the parameter space in such problems can be addressed with methods based on tensor decompositions and modelling. In recent work, we focused on a particular type of multilinear structure—namely the bilinear form (i.e., two-dimensional decompositions)—in the framework of identifying spatiotemporal models. In this paper, we extend the work to the decomposition of more complex systems and we propose an iterative Wiener filter tailored for the identification of trilinear forms (where third-order tensors are involved), which can then be further extended to higher order multilinear structures. In addition, we derive the least-mean-square (LMS) and normalized LMS (NLMS) algorithms tailored for such trilinear forms. Simulations performed in the context of system identification (based on the MISO system approach) indicate the good performance of the proposed solution, as compared to conventional approaches.

scholarly journals GEVD Based on Multichannel Wiener Filter for Removal of EEG Artifacts

2019 ◽  
Vol 8 (10) ◽  
pp. 2417-2421 ◽  
Keyword(s):  
Wiener Filter ◽  
Low Rank ◽  
Eeg Signals ◽  
Low Rank Approximation ◽  
Artifact Removal ◽  
Major Barrier ◽  
Eeg Data ◽  
Error Ratio ◽  
Eigen Value ◽  
Value Decomposition

The electroencephalography (EEG) signals are contaminated by ocular artifacts usually called as ElectroOculoGraphy(EOG) artifacts. This occurs due to an eye movement and repeatedly blinking eyes, it is a major barrier to overcome when analyzing ElectroEncephaloGram (EEG) data. In this paper, Generalized Eigen Value Decomposition (GEVD) algorithm based on Multichannel Wiener filter (MWF) was proposed. In the GEVD algorithm, the covariance matrix of the artifact is identified and substituted by low rank approximation. For both real and hybrid EEG data is demonstrated using this algorithm and also compared with other existing methods for removal of artifacts. This paper determines generic, robust and fast algorithm for artifact removal of various types of EEG signals. Signal to Error Ratio (SER) and Artifact to Residue Ratio (ARR) both are expressed in dBs. The better performance of artifact removal is expressed with high SER which measures clean EEG distortion and ARR measures the artifact estimation.

scholarly journals A Kalman Filter for Multilinear Forms and Its Connection with Tensorial Adaptive Filters

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3555
Author(s):  
Laura-Maria Dogariu ◽  
Constantin Paleologu ◽  
Jacob Benesty ◽  
Cristian-Lucian Stanciu ◽  
Claudia-Cristina Oprea ◽  
...  
Keyword(s):  
Kalman Filter ◽  
System Identification ◽  
Adaptive Filters ◽  
Wiener Filter ◽  
Decomposition Techniques ◽  
Identification Problems ◽  
Multilinear Forms ◽  
Wide Range ◽  
Low Dimension ◽  
The Individual

The Kalman filter represents a very popular signal processing tool, with a wide range of applications within many fields. Following a Bayesian framework, the Kalman filter recursively provides an optimal estimate of a set of unknown variables based on a set of noisy observations. Therefore, it fits system identification problems very well. Nevertheless, such scenarios become more challenging (in terms of the convergence and accuracy of the solution) when the parameter space becomes larger. In this context, the identification of linearly separable systems can be efficiently addressed by exploiting tensor-based decomposition techniques. Such multilinear forms can be modeled as rank-1 tensors, while the final solution is obtained by solving and combining low-dimension system identification problems related to the individual components of the tensor. Recently, the identification of multilinear forms was addressed based on the Wiener filter and most well-known adaptive algorithms. In this work, we propose a tensorial Kalman filter tailored to the identification of multilinear forms. Furthermore, we also show the connection between the proposed algorithm and other tensor-based adaptive filters. Simulation results support the theoretical findings and show the appealing performance features of the proposed Kalman filter for multilinear forms.

scholarly journals Tensor-Based Adaptive Filtering Algorithms

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 481
Author(s):  
Laura-Maria Dogariu ◽  
Cristian-Lucian Stanciu ◽  
Camelia Elisei-Iliescu ◽  
Constantin Paleologu ◽  
Jacob Benesty ◽  
...  
Keyword(s):  
System Identification ◽  
Impulse Response ◽  
Adaptive Filtering ◽  
Adaptive Filters ◽  
Performance Criteria ◽  
Multidimensional Data ◽  
Identification Problems ◽  
Filtering Algorithms ◽  
Single Output ◽  
Output System

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and the channels can be grouped in the form of rank-1 tensors. Nevertheless, the approach could be further extended for single-input/single-output system identification scenarios, where the impulse responses (of more general forms) can be modeled as higher-rank tensors. As compared to the conventional adaptive filters, which involve a single (usually long) filter for the estimation of the global impulse response, the tensor-based algorithms achieve faster convergence rate and tracking, while also providing better accuracy of the solution. Simulation results support the theoretical findings and indicate the advantages of the tensor-based algorithms over the conventional ones, in terms of the main performance criteria.

scholarly journals An Insightful Overview of the Wiener Filter for System Identification

2021 ◽  
Vol 11 (17) ◽  
pp. 7774
Author(s):  
Laura-Maria Dogariu ◽  
Jacob Benesty ◽  
Constantin Paleologu ◽  
Silviu Ciochină
Keyword(s):  
System Identification ◽  
Real World ◽  
Optimization Problems ◽  
Wiener Filter ◽  
Identification Problem ◽  
Low Rank ◽  
Regularization Methods ◽  
Noisy Environments ◽  
Regularization Technique ◽  
Theoretical Developments

Efficiently solving a system identification problem represents an important step in numerous important applications. In this framework, some of the most popular solutions rely on the Wiener filter, which is widely used in practice. Moreover, it also represents a benchmark for other related optimization problems. In this paper, new insights into the regularization of the Wiener filter are provided, which is a must in real-world scenarios. A proper regularization technique is of great importance, especially in challenging conditions, e.g., when operating in noisy environments and/or when only a low quantity of data is available for the estimation of the statistics. Different regularization methods are investigated in this paper, including several new solutions that fit very well for the identification of sparse and low-rank systems. Experimental results support the theoretical developments and indicate the efficiency of the proposed techniques.

Sign in / Sign up

Export Citation Format

Share Document