Complex-valued Wavelet Research Articles

Retracted: Singular Signal Measurement Based on Bidirectional Recursive Complex-Valued Wavelet Algorithm

Retracted: Singular Signal Measurement Based on Bidirectional Recursive Complex-Valued Wavelet Algorithm

Singular Signal Measurement Based on Bidirectional Recursive Complex-Valued Wavelet Algorithm

The normal operation fault of the power system is usually caused by a short-circuit fault. At this time, the system changes drastically from one state to another, accompanied by complex transient phenomena. Therefore, the measured signal contains a large number of transient components. How to effectively analyze such signals, extract their characteristics, and develop new protection devices has always been an important research field in power system protection technology. The protection of the power system is to achieve the purpose of correct action and elimination of faults by quickly detecting and locating faults. At present, the power signal analysis tools used in microcomputer protection include FFT, Kalman filter, and finite impulse response filter. They are efficient for the analysis of stationary signals, but have their limitations in analyzing nonstationary signals; especially it is difficult to identify nonlinear faults, such as the detection of high-impedance nonlinear short-circuit faults, which is a long-term unsolved problem in power systems. Based on wavelet transform, this paper selects complex-valued wavelet algorithm, analyzes a real-time recursive wavelet algorithm, and deduces the realization process of the algorithm in detail. The algorithm greatly reduces the computational complexity of the existing two-way recursive algorithm, can be used for real-time detection of fault signals in various fields of power system, and can be extended to realize other fast recursive algorithms of wavelet functions. Based on the sensitivity of complex-valued wavelet transform phase information to singularity, a method for real-time monitoring of power system fault mutation signals using the phase information of complex-valued wavelet fast recursion algorithm to assist amplitude information is proposed. The validity and practicability of this complex-valued wavelet and its real-time recursive algorithm for fault detection are demonstrated by an example.

Complex-Valued Wavelet Spectrum Analysis of Respiratory Conditions and Its Feasibility in the Detection of Low-Functional Respiration.

Respiratory monitoring is a significant issue to reduce patient risks and medical staff labor in postoperative care and epidemic infection, particularly after the COVID-19 pandemic. Oximetry is widely used for respiration monitoring in the clinic, but it sometimes fails to capture a low-functional respiratory condition even though a patient has breathing difficulty. Another approach is breathing-sound monitoring, but this is unstable due to the indirect measurement of lung volume. Kobayashi in our team is developing a sensor measuring temporal changes in lung volume with a displacement sensor attached across the sixth and eighth ribs. For processing these respiratory signals, we propose the combination of complex-valued wavelet transform and the correlation among spectrum sequences. We present the processing results and discuss its feasibility to detect a low-functional condition in respiration. The result for detecting low-functional respiration showed good performance with a sensitivity of 0.88 and specificity of 0.88 to 1 in its receiver operating characteristic (ROC) curve.

Image inpainting using directional wavelet packets originating from polynomial splines

The paper presents a new algorithm for the image inpainting problem. The algorithm uses a recently designed versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of these qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which expands the Split Bregman Iteration (SBI) procedure by supplying it with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.

Classification of hyperspectral imagery using a fully complex-valued wavelet neural network with deep convolutional features

The number of spectral bands obtained by hyperspectral sensors improves the ability to distinguish physical objects and materials. But it also brings new challenges to image classification and analysis. In this study, a novel deep learning-based hybrid model called CNN-CVWNN is presented for the hyperspectral images classification (HSIs). The model uses a convolutional neural network (CNN) to extract multilayer image representation and uses the complex valued wavelet neural network (CVWNN) to classify the image using extracted features. The process steps of the proposed method are briefly as follows. First of all, the CNN algorithm has been applied to hyperspectral images. After this stage, efficient features have been obtained. These extracted features were then converted into a complex-valued number format using a novel random based transformation method. Thus, a novel complex-valued attribute set has been obtained for the HSI classification. The obtained features have been presented as input to the CVWNN algorithm. The hybrid method replaces real valued neural network inside CNN with CVWNN to enhance robustness and generalization of CNN. The experiments have been carried out on three data sets consisted of three popular hyperspectral airborne images. The developed method increases classification accuracy compared to other classification approaches.

R-R Interval Estimation for Wearable Electrocardiogram Based on Single Complex Wavelet Filtering and Morphology-Based Peak Selection

Recent innovations in wearable electrocardiogram (ECG) devices have enabled various personal healthcare applications based on heart rate variability (HRV). However, wearable ECGs rarely undergo visual inspection by medical experts, hence may contain noise and artifacts. Because apparent changes in the recorded ECGs caused by noise and artifacts may hamper the extraction of QRS complexes, an R-R interval (RRI) estimation algorithm tolerant to these measurement faults is required as the initial step toward HRV analysis using wearable ECGs. This paper proposes a semi-real-time RRI estimation for wearable ECGs utilizing a two-stage structure. In the preprocessing stage, we use a complex-valued wavelet that can adaptively fit to morphological variations of the QRS complex while retaining computing resources for extracting the QRS complex features. In the decision stage, we make use of complex-valued features and select appropriate QRS complexes in consideration of three features: peak magnitude, peak location, and peak morphology (phase). Initial evaluations show that the QRS complex detection performance of the proposed method achieved the F1 score of 0.952 ± 0.040 when targeting pseudo ECG data created from open data assuming wearable ECGs, and of 0.986 ± 0.018 when targeting actual ECG data recorded by a shirt-type wearable ECG device during an exercise activity. Furthermore, the proposed method was able to suppress overlook or misdetection of QRS complexes, so the obtained RRIs are closer to the reference RRIs. The proposed method therefore contributes to achieving accurate HRV analysis using wearable ECGs in terms of obtaining accurate RRIs.

Characterization of twist of fancy yarns using wavelet analysis of sensor signal

Yarn twist variations may cause stripes in the direction of weft yarns or local defects on a fabric surface. Since fast Fourier transform and time analysis cannot directly detect local frequency variations of yarn signal and defect sensors are designed to detect the diameter decreases without considering frequency analysis, no data associated with twist-related frequency changes can be obtained when inspecting Chenille yarn (Cy) defects. This study proposes the prediction of twist level ( T) and twist variations ( ΔT) of Cy whose twist changes in accordance with the spatial period of pile density by using wavelet analysis, allowing localized frequency variations to be obtained. Complex-valued Paul wavelet was used to determine the ΔT of signals with small frequency fluctuations, while Morlet wavelet was addressed for signals with high frequency change. The relation of the signal frequency to the pile yarn density and, correspondingly, twist was modeled by equations. To prevent discontinuities in wavelet cross-spectrum (WCS), the twist simulation signal was generated by equalizing twist oscillation amplitudes without changing their phase. To compare ideal twist to the local twist, another simulation signal demonstrating the ideal twist at sample-specific frequency was generated. The WCS of the simulation signals allowing the segmentation of variation intervals was used for determining ΔT and yarn portions, where the twist is compatible with ideal twist, by establishing correlation between scales and twists. For yarn samples with various T and ΔT types, the T and ΔT results obtained by the proposed wavelet-based algorithm showed the mean absolute relative percentage errors of 1.617% and 37.062%, respectively.

Extending the depth of field for ptychography using complex-valued wavelets: publisher's note.

This publisher's note corrects an error in Eq.(3) of Opt. Lett.44, 503 (2019).OPLEDP0146-959210.1364/OL.44.000503.

Extending the depth of field for ptychography using complex-valued wavelets.

Ptychography is a scanning variation of the coherent diffractive imaging method for providing high-resolution quantitative images from specimen with extended dimensions. Its capability of achieving diffraction-limited spatial resolution can be compromised by the sample thickness, which is generally required to be thinner than the depth of field of the imaging system. In this Letter, we present a method to extend the depth of field for ptychography by numerically generating the focus stack from reconstructions with propagated illumination wavefronts and combining the in-focus features to a single sharp image using an algorithm based on the complex-valued discrete wavelet transform. This approach does not require repeated measurements by translating the sample along the optical axis as in the conventional focus stacking method, and offers a computation-efficient alternative to obtain high-resolution images with extended depth of fields, complementary to the multi-slice ptychography.

Classification of sonar echo signals in their reduced sparse forms using complex-valued wavelet neural network

This study aims to identify a method for classifying signals using their reduced sparse forms with a higher degree of accuracy. Many signals, such as sonar, radar, or seismic signals, are either sparse or can be made sparse in the sense that they have sparse or compressible representations when expressed in the appropriate basis. They have a convenient transform domain in which a small number of sparse coefficients express them as linear sums of sinusoidals, wavelets, or other bases. Although real-valued artificial neural networks (ANNs) have been frequently used in the classification of sonar signals for a long time, complex-valued wavelet neural network (CVWANN) is used for these complex reduced sparse forms of sonar signals in this study. Before the classification, the number of inputs was reduced to 1/3 dimension. Complex-valued sparse coefficients (CVSCs) obtained from the reduced form were classified by CVWANN. The performance of the proposed method is presented and compared to other classification methods. Our method, CVSCs + CVWANN, is very successful as 94.23% by tenfold cross-validation data selection and 95.19% by 50–50% training–testing data selection.

A novel extended depth of field process based on nonsubsampled shearlet transform by estimating optimal range in microscopic systems

Abstract Increasing the depth of field (DOF) and maintain a high resolution have been the classical challenges for acquiring a single 2D image sample investigated with the microscope to enhance a complete in-focus. The extended depth-of-field microscope is implemented to overcome these problems. Various studies have proposed the wavefront coding and image fusion as the remedies for the blurred content of the in-focus image. In this study, a classical extended depth of field (EDOF) process based on the image fusion is implemented by moving a microscope platform along the fixed range, a distance between initial and final positions, to determine a random Z axis. During the movement of the platform in this range, a certain number of multi-focus images are acquired at infinite steps ( Δ d). However, it is seen that the magnification objective affects the range and number of the multi-focus images. Instead of determining the range randomly, the optimal range is selected to extract a significant information from the multi-focus images. In this study, a novel EDOF process based on the multi-scale representations is improved, estimating the optimal range in the microscopic systems. Our proposed EDOF process is performed in two main stages: pre-process and image fusion. In the pre-processing stage, various ranges with different initial and final positions are extracted to scan the whole structure of the sample on the Z axis. In the second stage, a novel image fusion approach based on the Nonsubsampled Shearlet transform (NSST) is implemented into all ranges to obtain the optimal fused image. To evaluate the performances of the proposed image fusion approach and to show the effects of other color spaces on the image fusion approaches based on the multi-scale representations, fused images created with the different fusion approaches including Maximum Absolute Selection, Variance, Tenengrad, Discrete Complex Valued Wavelet Transform, Discrete Curvelet Transform, and other color spaces (HSV, YIQ and YCbCr) are tested in terms of their transferred focus information, outliers and blurring. From the obtained experimental results, the fused image created with our proposed approach contains more detailed information and fewer outliers and artifacts. Furthermore, the YCbCr and HSV color models provide the highest performances that capture the critical information in terms of focusing.

A review of Morlet wavelet analysis of radial profiles of Saturn's rings.

Spiral waves propagating in Saturn's rings have wavelengths that vary with radial position within the disc. The best-quality observations of these waves have the form of radial profiles centred on a particular azimuth. In that context, the wavelength of a given spiral wave is seen to change substantially with position along the one-dimensional profile. In this paper, we review the use of Morlet wavelet analysis to understand these waves. When signal to noise is high and the cause of the wave is well understood, wavelet analysis has been used to solve for wave parameters that are diagnostic of local disc properties. Waves that are not readily perceptible in the spatial domain signal can be clearly identified. Furthermore, filtering in wavelet space, followed by the reverse wavelet transform, has been used to isolate the part of the signal that is of interest. When the cause of the wave is not known, comparing the phases of the complex-valued wavelet transforms from many profiles has been used to determine wave parameters that cannot be determined from any single profile. When signal to noise is low, co-adding wavelet transforms while manipulating the phase has been used to boost a wave's signal above detection limits.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Long memory estimation for complex-valued time series

Long memory has been observed for time series across a multitude of fields, and the accurate estimation of such dependence, for example via the Hurst exponent, is crucial for the modelling and prediction of many dynamic systems of interest. Many physical processes (such as wind data) are more naturally expressed as a complex-valued time series to represent magnitude and phase information (wind speed and direction). With data collection ubiquitously unreliable, irregular sampling or missingness is also commonplace and can cause bias in a range of analysis tasks, including Hurst estimation. This article proposes a new Hurst exponent estimation technique for complex-valued persistent data sampled with potential irregularity. Our approach is justified through establishing attractive theoretical properties of a new complex-valued wavelet lifting transform, also introduced in this paper. We demonstrate the accuracy of the proposed estimation method through simulations across a range of sampling scenarios and complex- and real-valued persistent processes. For wind data, our method highlights that inclusion of the intrinsic correlations between the real and imaginary data, inherent in our complex-valued approach, can produce different persistence estimates than when using real-valued analysis. Such analysis could then support alternative modelling or policy decisions compared with conclusions based on real-valued estimation.

Enhanced frame expansion via configuring filterbank topology for rapid processing of multi-sensor vibration data with applications to turbo-machinery fault diagnosis

Multi-sensor deployment is usually utilized in recent structural health monitoring of rotating machinery. Conventional wavelet transform is widely applied in relevant data processing tasks. However, wavelet transform still suffers from deficiencies such as lacking of frequency adjustability and shift variance property. In this article, an enhanced frame expansion is constructed via filterbank topology approach, which addresses these problems but at the same time can be implemented via fast numerical algorithm. In this scheme, different discrete complex wavelet frames are deployed at different processing stages within the filterbank structure. Enhanced frame expansion is obtained via integration of multiple translation-invariant frames. The derived timescale analyzing properties of enhanced frame expansion, whose wavelet functions form approximate Hilbert transform pairs, were investigated. It is also verified that the enhanced frame expansion satisfies the necessary constraints of complex-valued wavelet frame and other beneficial merits. Another major advantage presented by the enhanced frame expansion, which is different from complex-valued wavelet frame, dwells in its nondyadic frequency-scale paving. Moreover, the constructed enhanced frame expansion is also of low computational burden due to its inheriting of tree structure filterbank. The proposed enhanced frame expansion is applied to vibration feature extraction from multi-sensor data of a turbo-machinery. The processing results from the displacement signal as well as the acceleration signal indicate the rub-impact fault.

Complex-Valued Wavelet Lifting and Applications

ABSTRACTSignals with irregular sampling structures arise naturally in many fields. In applications such as spectral decomposition and nonparametric regression, classical methods often assume a regular sampling pattern, thus cannot be applied without prior data processing. This work proposes new complex-valued analysis techniques based on the wavelet lifting scheme that removes “one coefficient at a time.” Our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal(s)’ characteristics. As our new lifting scheme produces complex-valued wavelet coefficients, it provides an alternative to the Fourier transform for irregular designs, allowing phase or directional information to be represented. We discuss applications in bivariate time series analysis, where the complex-valued lifting construction allows for coherence and phase quantification. We also demonstrate the potential of this flexible methodology over real-valued analysis in the nonparametric regression context. Supplementary materials for this article are available online.

A convolutional approach to reflection symmetry

We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on the products of complex-valued wavelet convolutions, simplifies previous edge-based pairwise methods. Being parameter-centered, as opposed to feature-centered, it has certain computational advantages when the object sizes are known a priori, as demonstrated in an ellipse detection application. The method outperforms the best-performing algorithm on the CVPR 2013 Symmetry Detection Competition Database in the single-symmetry case. We release code and a new, larger image database.

Real and complex wavelets in asset classification: An application to the US stock market

In the paper we suggest the use of wavelets to classify equities and industries into defensive and cyclical categories. We demonstrate that real- and complex-valued wavelets better serve the purpose of equity classification than more traditional approaches, and that this takes place through a more reliable and detailed dependence measurement and risk assessment. In particular, we introduce a family of wavelet-based tests of the random walk hypothesis exploring local features of spectra, which enable examining mean reversion and cyclicality of prices. The suggested approach is illustrated with an analysis of daily and monthly US industry indexes.

Real- and Complex-Valued Discrete Wavelets in Asset Classification. Some Methodological Remarks with Example

Real- and Complex-Valued Discrete Wavelets in Asset Classification. Some Methodological Remarks with Example

Image denoising with 2D scale-mixing complex wavelet transforms.

This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions that preserve the phase of the complex-valued wavelet coefficients and those that do not. The new procedure exhibits excellent quantitative and visual performance, which is demonstrated by simulation on standard test images.

The New Complex-Valued Wavelet Neural Network

A new complex-valued wavelet neural network is proposed in this paper, by introducing a modified complex-valued back propagation algorithm, in which a new error function is to be minimized by the algorithm. The improvement performance is further confirmed by the simulation results, which show that the modified algorithm is simpler than the conventional algorithm, and has better convergence, better stability and faster running speed.