Quaternion-based sparse tight frame for multicomponent signal recovery

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V143-V156
Author(s):  
Qiang Zhao ◽  
Qizhen Du ◽  
Qamar Yasin ◽  
Qingqing Li ◽  
Liyun Fu
Keyword(s):  
Random Noise ◽  
Tight Frame ◽  
Signal Recovery ◽  
Weak Signals ◽  
Multicomponent Signal ◽  
Scalar Data ◽  
Multicomponent Signals ◽  
Improved Performance ◽  
Value Decomposition ◽  
Multicomponent Data

Multicomponent noise attenuation often presents more severe processing challenges than scalar data owing to the uncorrelated random noise in each component. Meanwhile, weak signals merged in the noise are easier to degrade using the scalar processing workflows while ignoring their possible supplement from other components. For seismic data preprocessing, transform-based approaches have achieved improved performance on mitigating noise while preserving the signal of interest, especially when using an adaptive basis trained by dictionary-learning methods. We have developed a quaternion-based sparse tight frame (QSTF) with the help of quaternion matrix and tight frame analyses, which can be used to process the vector-valued multicomponent data by following a vectorial processing workflow. The QSTF is conveniently trained through iterative sparsity-based regularization and quaternion singular-value decomposition. In the quaternion-based sparse domain, multicomponent signals are orthogonally represented, which preserve the nonlinear relationships among multicomponent data to a greater extent as compared with the scalar approaches. We test the performance of our method on synthetic and field multicomponent data, in which component-wise, concatenated, and long-vector models of multicomponent data are used as comparisons. Our results indicate that more features, specifically the weak signals merged in the noise, are better recovered using our method than others.

scholarly journals Sparse Signal Recovery from Modulo Observations

2020 ◽  
Author(s):  
Viraj Shah ◽  
Chinmay Hegde
Keyword(s):  
Phase Retrieval ◽  
Dynamic Range ◽  
Signal Reconstruction ◽  
Real Data ◽  
Superior Performance ◽  
Signal Recovery ◽  
Reconstruction Methods ◽  
Novel Approach ◽  
Sparsity Constraints ◽  
Improved Performance

Abstract We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the inverse problem limited to two modulo periods, inspired by recent advances in algorithms for phase retrieval under sparsity constraints. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal and provides improved performance over other existing algorithms. We also provide experiments validating our approach on both synthetic and real data to depict its superior performance.

scholarly journals A Signal Complexity-Based Approach for AM–FM Signal Modes Counting

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2170
Author(s):  
Vittoria Bruni ◽  
Michela Tartaglione ◽  
Domenico Vitulano
Keyword(s):  
Instantaneous Frequency ◽  
Individual Component ◽  
Stationary Process ◽  
Practical Applications ◽  
Time Frequency ◽  
Number Of Components ◽  
Multicomponent Signal ◽  
Multicomponent Signals ◽  
Robustness To Noise ◽  
Signal Complexity

Frequency modulated signals appear in many applied disciplines, including geology, communication, biology and acoustics. They are naturally multicomponent, i.e., they consist of multiple waveforms, with specific time-dependent frequency (instantaneous frequency). In most practical applications, the number of modes—which is unknown—is needed for correctly analyzing a signal; for instance for separating each individual component and for estimating its instantaneous frequency. Detecting the number of components is a challenging problem, especially in the case of interfering modes. The Rényi Entropy-based approach has proven to be suitable for signal modes counting, but it is limited to well separated components. This paper addresses this issue by introducing a new notion of signal complexity. Specifically, the spectrogram of a multicomponent signal is seen as a non-stationary process where interference alternates with non-interference. Complexity concerning the transition between consecutive spectrogram sections is evaluated by means of a modified Run Length Encoding. Based on a spectrogram time-frequency evolution law, complexity variations are studied for accurately estimating the number of components. The presented method is suitable for multicomponent signals with non-separable modes, as well as time-varying amplitudes, showing robustness to noise.

scholarly journals Multicomponent MR Image Denoising

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
José V. Manjón ◽  
Neil A. Thacker ◽  
Juan J. Lull ◽  
Gracian Garcia-Martí ◽  
Luís Martí-Bonmatí ◽  
...  
Keyword(s):  
Random Noise ◽  
Principal Component ◽  
Magnetic Resonance Images ◽  
Image Resolution ◽  
Single Image ◽  
Mr Images ◽  
Mr Image ◽  
Automatic Feature Extraction ◽  
Improved Performance ◽  
Multicomponent Nature

Magnetic Resonance images are normally corrupted by random noise from the measurement process complicating the automatic feature extraction and analysis of clinical data. It is because of this reason that denoising methods have been traditionally applied to improve MR image quality. Many of these methods use the information of a single image without taking into consideration the intrinsic multicomponent nature of MR images. In this paper we propose a new filter to reduce random noise in multicomponent MR images by spatially averaging similar pixels using information from all available image components to perform the denoising process. The proposed algorithm also uses a local Principal Component Analysis decomposition as a postprocessing step to remove more noise by using information not only in the spatial domain but also in the intercomponent domain dealing in a higher noise reduction without significantly affecting the original image resolution. The proposed method has been compared with similar state-of-art methods over synthetic and real clinical multicomponent MR images showing an improved performance in all cases analyzed.

scholarly journals REGULARIZATION STRATEGIES FOR HYPERPLANE CLASSIFIERS: APPLICATION TO CANCER CLASSIFICATION WITH GENE EXPRESSION DATA

2007 ◽  
Vol 05 (01) ◽  
pp. 79-104 ◽  
Author(s):  
ERIK ANDRIES ◽  
THOMAS HAGSTROM ◽  
SUSAN R. ATLAS ◽  
CHERYL WILLMAN
Keyword(s):  
Gene Expression ◽  
Gene Expression Data ◽  
Linear Equations ◽  
Numerical Linear Algebra ◽  
Point Of View ◽  
Diagnostic Tools ◽  
Expression Data ◽  
Linear Discrimination ◽  
Improved Performance ◽  
Value Decomposition

Linear discrimination, from the point of view of numerical linear algebra, can be treated as solving an ill-posed system of linear equations. In order to generate a solution that is robust in the presence of noise, these problems require regularization. Here, we examine the ill-posedness involved in the linear discrimination of cancer gene expression data with respect to outcome and tumor subclasses. We show that a filter factor representation, based upon Singular Value Decomposition, yields insight into the numerical ill-posedness of the hyperplane-based separation when applied to gene expression data. We also show that this representation yields useful diagnostic tools for guiding the selection of classifier parameters, thus leading to improved performance.

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.

Principal component transforms of triaxial recordings by singular value decomposition

Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 528-533 ◽  
Author(s):  
G. M. Jackson ◽  
I. M. Mason ◽  
S. A. Greenhalgh
Keyword(s):  
Singular Value Decomposition ◽  
Time Window ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Principal Component ◽  
Singular Value ◽  
Data Matrix ◽  
Single Station ◽  
Window Selection ◽  
Value Decomposition

Polarization analysis can be achieved efficiently by treating a time window of a single‐station triaxial recording as a matrix and doing a singular value decomposition (SVD) of this seismic data matrix. SVD of the triaxial data matrix produces an eigenanalysis of the data covariance (cross‐energy) matrix and a rotation of the data onto the directions given by the eigenanalysis (Karhunen‐Loève transform), all in one step. SVD provides a complete principal components analysis of the data in the analysis time window. Selection of this time window is crucial to the success of the analysis and is governed by three considerations: the window should contain only one arrival; the window should be such that the signal‐to‐noise ratio is maximized; and the window should be long enough to be able to discriminate random noise from signal. The SVD analysis provides estimates of signal, signal polarization directions, and noise. An F‐test is proposed which gives the confidence level for the hypothesis of rectilinear polarization. This paper illustrates the analysis and interpretation of synthetic rectilinearly and elliptically polarized arrivals at a single triaxial station by SVD.

scholarly journals The face is central to primate multicomponent signals

2022 ◽  
Author(s):  
Bridget M. Waller ◽  
Eithne Kavanagh ◽  
Jerome Micheletta ◽  
Peter R. Clark ◽  
Jamie Whitehouse
Keyword(s):  
A Priori ◽  
Detailed Examination ◽  
Visual Component ◽  
Multimodal Signals ◽  
Multicomponent Signal ◽  
Multicomponent Signals ◽  
The Face ◽  
Facial Behavior ◽  
Dynamic Components

AbstractA wealth of experimental and observational evidence suggests that faces have become increasingly important in the communication system of primates over evolutionary time and that both the static and moveable aspects of faces convey considerable information. Therefore, whenever there is a visual component to any multicomponent signal the face is potentially relevant. However, the role of the face is not always considered in primate multicomponent communication research. We review the literature and make a case for greater focus on the face going forward. We propose that the face can be overlooked for two main reasons: first, due to methodological difficulty. Examination of multicomponent signals in primates is difficult, so scientists tend to examine a limited number of signals in combination. Detailed examination of the subtle and dynamic components of facial signals is particularly hard to achieve in studies of primates. Second, due to a common assumption that the face contains “emotional” content. A priori categorisation of facial behavior as “emotional” ignores the potentially communicative and predictive information present in the face that might contribute to signals. In short, we argue that the face is central to multicomponent signals (and also many multimodal signals) and suggest future directions for investigating this phenomenon.

Research on Fault Feature Extraction Method of the Wind Turbine Gearbox Based on SVD and Improved HHT

2012 ◽  
Vol 220-223 ◽  
pp. 785-788
Author(s):  
Chang Zheng Chen ◽  
Quan Gu ◽  
Bo Zhou
Keyword(s):  
Feature Extraction ◽  
Singular Value Decomposition ◽  
Wind Turbine ◽  
Extraction Method ◽  
Random Noise ◽  
Singular Value ◽  
Wind Turbine Gearbox ◽  
Feature Extraction Method ◽  
Value Decomposition ◽  
Fault Feature Extraction

This paper researches fault feature extraction method based on singular value decomposition and the improved HHT method for non-stationary characteristics of wind turbine gearbox vibration signal. Firstly, through the signal phase space reconstruction, the singular value decomposition as a pre-filter, to preprocessing the signal, effectively weaken the random noise. Then using EEMD to improve the HHT method, decompose the denoising signal into a series of different time scales component of intrinsic mode functions. The fault characteristics of the signal are extracted by the Hilbert transform. Finally, simulating gearbox fault experiment to verify the effectively of the proposed method.

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