Multidimensional Wavelet Research Articles

Differentiating Glioblastoma Multiforme from Brain Metastases Using Multidimensional Radiomics Features Derived from MRI and Multiple Machine Learning Models.

Due to different treatment strategies, it is extremely important to differentiate between glioblastoma multiforme (GBM) and brain metastases (MET). It often proves difficult to distinguish between GBM and MET using MRI due to their similar appearance on the imaging modalities. Surgical methods are still necessary for definitive diagnosis, despite the importance of magnetic resonance imaging in detecting, characterizing, and monitoring brain tumors. We introduced an accurate, convenient, and user-friendly method to differentiate between GBM and MET through routine MRI sequence and radiomics analyses. We collected 91 patients from one institution, including 50 with GBM and 41 with MET, which were proven pathologically. The tumors separately were segmented on all MRI images (T1-weighted imaging (T1WI), contrast-enhanced T1-weighted imaging (T1C), T2-weighted imaging (T2WI), and fluid-attenuated inversion recovery (FLAIR)) to form the volume of interest (VOI). Eight ML models and feature reduction strategies were evaluated using routine MRI sequences (T1W, T2W, T1-CE, and FLAIR) in two methods with (second model) and without wavelet transform (first model) radiomics. The optimal model was selected based on each model's accuracy, AUC-roc, and F1-score values. In this study, we have achieved the result of 0.98, 0.99, and 0.98 percent for accuracy, AUC-roc, and F1-score, respectively, which have yielded a better result than the first model. In most investigated models, there were significant improvements in the multidimensional wavelets model compared to the non-multidimensional wavelets model. Multidimensional discrete wavelet transform can analyze hidden features of the MRI from a different perspective and generate accurate features which are highly correlated with the model accuracy.

Wavelet-Based Multiscale Decomposition Algorithm for Trajectory Capture of Tennis Serves.

Tennis is a sport that is enjoyed by young and old alike. Participants can decide the style of play and control the speed and spin of the ball according to their ability, so the physical demands on participants are not high and the amount of exercise can be effectively controlled. With the increasing demand for quality of life, the population of tennis is growing rapidly. People have taken up tennis as a form of recreation. For professional players, the serve, as the foundation of the introduction to tennis, has been a challenge. A good serve can effectively control the situation on the court and even turn defeat into victory. Therefore, this paper focuses on capturing tennis trajectories using multidimensional wavelet segmentation in an attempt to provide an effective reference for tennis. The results show that our method has a good trajectory capturing effect and can correct and guide the tennis serving action well.

On the space of periodic distributions with multi-dimensional wavelet packet transform

On the space of periodic distributions with multi-dimensional wavelet packet transform

Analysis of multivariate time series for some linear models by using multi-dimensional wavelet shrinkage

The wavelet transform for multivariate time-series analysis and prediction is performed using an automatic slow distribution model and the prediction accuracy is compared with the normal method through the use of statistical criteria. By taking the variables represented by the gross domestic product as a response variable and air pollutants as explanatory variables represented by the emissions of nitrous oxide and carbon dioxide in Iraq. The study showed that there is an inverse relationship between the emissions of carbon dioxide and gross domestic product, while a positive relationship between the emissions of nitrous oxide and gross domestic product. And that the variables analysis and prediction after performing the wavelet transform of the data is the best because it contains the lowest values of the mean square error criterion and the mean criterion of absolute error.

Decoherence-Optimized Circuits for Multidimensional and Multilevel-Decomposable Quantum Wavelet Transform

Algorithms such as quantum wavelet transform (QWT) can be utilized on quantum processors to gain significant speedup compared to their classical counterparts. Domains such as high-energy-physics and remote-sensing hyperspectral imagery require high compute capabilities and can benefit from applying QWT for dimension reduction of multidimensional data. However, quantum circuits for QWT include permutations that contribute to large overall circuit depth. Deep circuits pose a critical challenge for state-of-the-art quantum computers because of quantum decoherence. In this work, we propose QWT circuits, which are optimized in terms of circuit depth, to account for the effects of decoherence, and resulting in high fidelity and efficient implementation on quantum processors. We present the circuits in generalized forms and show that they can be used for multilevel decomposable, multidimensional wavelet operations. Experimental evaluation of the proposed circuits is performed through simulation using MATLAB and IBM-Q qasm, and implemented on a real 15-qubit quantum processor from IBM.

A design of laser array harp based on multi-dimensional wavelet transform and audio signal reconstruction

This paper introduces a design scheme of laser array harp based on multi-dimensional wavelet transform and audio signal reconstruction. The green light beams from multiple high-power lasers simulate harp strings, use photoresistors as the signal receiving end, and use a signal conditioning system composed of analog circuits and LM393 comparators to collect and adjust the resistance signal of the laser sensor[1], and finally it is adjusted to a level signal that can be recognized by the CPU. After receiving the signal, the CPU core board analyzes the string signal, and sends control commands to the audio processing system through the industrial bus according to the analyzed digital signal. After receiving the control command, the audio processing system uses the audio signal reconstruction technology composed of multi-dimensional wavelet packets, deep learning and other algorithms to simulate the audio signals of various string music, so as to achieve the purposes of using the lasers as virtual strings and imitating musical instruments for musical performance.[2]

Single upper limb functional movements decoding from motor imagery EEG signals using wavelet neural network

In this study, we propose a wavelet neural network (WNN) to improve the performance of movements decoding from motor imagery (MI) EEG signals. Fifteen healthy subjects performed six functional movements of single upper limb: forearm pronation/supination, hand open/close, and elbow flexion/extension. The wavelet packet decomposition (WPD) was used to decompose MI EEG into sub-bands, and the statistical features were extracted from the sub-bands to code the functional movements. Subsequently, the principal component analysis (PCA) was used to select the best feature vector. The factors of mother wavelet, multidimensional wavelet function, number of channels, and the time of imaging segment were optimized through experiments. As a result, the best accuracy of 86.27 ± 6.98% was achieved with the optimized coif1 mother wavelet with a six-level decomposition, Mexican Hat wavelet as a hyperparameter, the time of imaging segment set as 0.7 s, and 61 channels data. In addition, to further verify the efficiency of the WNN classifier, the comparative experiments were conducted with the support vector machine (SVM), linear discriminant analysis (LDA), k-nearest neighbor (KNN), and single hidden layer feedforward neural network (ANN). The results show that the accuracy of WNN is improved by about 15 ~ 40%, which proved the effectiveness of the WNN method. This study provides a new way to decode from motor imagery EEG in multi-movement classification.

Posterior contraction and credible regions for level sets

For a given function f on a multivariate domain, the level sets, given by {x:f(x)=c} for different values of c, provide important geometrical insights about the underlying function of interest. The distance on level sets of two functions may be measured by the Hausdorff metric or a metric based on the Lebesgue measure of a discrepancy, both of which can be linked with the L∞-distance on the underlying functions. In a Bayesian framework, we derive posterior contraction rates and optimal sized credible sets with assured frequentist coverage for level sets in some nonparametric settings by extending some univariate L∞-posterior contraction rates to the corresponding multivariate settings. For the multivariate Gaussian white noise model, adaptive Hausdorff and Lebesgue contraction rates for levels sets of the signal function and its mixed order partial derivatives are derived using a wavelet series prior on the function. Assuming a known smoothness level of the signal function, an optimal sized credible region for a level set with assured frequentist coverage is derived based on a multidimensional trigonometric series prior. For the nonparametric regression problem, adaptive rates for level sets of the function and its mixed partial derivatives are obtained using a multidimensional wavelet series prior. When the smoothness level is given, optimal sized credible regions with assured frequentist coverage are obtained using a finite random series prior based on tensor products of B-splines. We also derive Hausdorff and Lebesgue contraction rates of a multivariate density function under a known smoothness setting.

Sufficient Conditions for a Multidimensional System of Periodic Wavelets to be a Frame

We study multidimensional periodic wavelet systems with matrix dilations. We obtain conditions sufficient for such a system to be Bessel. The conditions are given in terms of Fourier coefficients. We propose a method for constructing a wavelet Riesz basis that starts with a suitable sequence of trigonometric polynomials.

An efficient multidimensional $L_{\infty }$ wavelet method and its application to approximate query processing

Approximate query processing (AQP) has been an effective approach for real-time and online query processing for today’s query systems. It provides approximate but fast query results to users. In wavelet based AQP, queries are executed against the wavelet synopsis which is a lossy, compressed representation of the original data returned by a specific wavelet method. Wavelet synopsis optimized for $L_{\infty }$ -norm error can guarantee approximate error of each individual element, thus it can provide error guaranteed query results for many queries. However, most algorithms for building one dimensional $L_{\infty }$ synopsis are of super linear complexity, which makes the extension to their multidimensional case challengeable. In this paper, we propose an efficient multidimensional wavelet method towards constructing $L_{\infty }$ synopsis and we apply it to AQP. The proposed wavelet method can bound the approximate error of each individual element and it has linear time complexity. It can also provide fast AQP. These good properties are all verified theoretically. Extensive experiments on both synthetic and real-life datasets are presented to show its effectiveness and efficiency for data compression and AQP.

Multi-dimensional wavelets for scalable image decomposition: Orbital wavelets

Wavelets are closely related to Schrödinger’s wave functions and the interpretation of Born. Similar to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach allows the increase of the dimension of wavelets through this process. New orbital 2D-wavelets are introduced for the decomposition of still images, showing that it is possible to perform an analysis simultaneously in two distinct scales. An example of such an image analysis is shown.

Fault Recovery Path Analysis of a Software Dynamic Image Based on a Fuzzy Control Algorithm

In order to improve the ability of software dynamic image fault detection, a software dynamic image fault recovery path detection algorithm based on a fuzzy control algorithm is proposed. A software dynamic image fault signal model of a software dynamic image fault was constructed by adopting an embedded feature extraction and a fuzzy control algorithm, and the dynamic image fault signal of the embedded software under the multi-load was subjected to frequency spectrum decomposition and blind source separation. The method comprises the following steps: (1) carrying out noise reduction processing on a software dynamic image fault signal by adopting a multi-dimensional wavelet decomposition method, (2) carrying out wavelet entropy feature extraction on the software dynamic image fault signal of the noise reduction output, and (3) combining the wavelet structural feature recombination method to carry out the recombination of the software dynamic image fault feature. The high-order spectral characteristic of the software dynamic image fault signal was extracted and the high-order spectral characteristic of the extracted embedded software dynamic image fault recovery path was automatically matched, and the automatic identification and detection of the fault part of the software dynamic image was realized.

Multi-dimensional wavelet reduction for the homogenisation of microstructures

One of the recent fields of interest in computational homogenisation is the development of model order reduction frameworks to address the significant computational costs enabling fast and accurate evaluation of the microstructural volume element. Model order reduction techniques are applied to computationally challenging analyses of detailed micro- and or macro-structural problems to reduce both computational time and memory usage. In order to alleviate the costly integration, a wavelet-reduced order model for one-dimensional microstructural problems was presented in van Tuijl et al. (2019). This novel approach addresses both the large number of degrees of freedom and integration costs and provides control on errors in the microstructural fields. In this work, this wavelet reduced order model is extended to a multi-dimensional framework and benchmarked for more realistic multi-scale problems.The Wavelet-Reduced Order Model consists of two reduction steps. First, a Reduced Order Model is constructed to reduce the dimensionality of the microstructural model. Second, a wavelet representation is applied to reduce the integration costs of the microstructural model, whilst maintaining control over the local integration error. The multi-dimensional Wavelet-Reduced Order Model is demonstrated for a set of two-dimensional path-dependent microstructural models, evaluating their accuracy and reduction with respect to the full order models on the microstructural and homogenised fields.

A Novel Algorithm for Hyperspectral Image Denoising in Medical Application.

The one of the preprocessing step for hyperspectral imagery is noise reduction. The images are received by the detector and this can be degraded by several factors like atmospherical things and device noises which emit temperature noise, processing noise and explosion noise. There are several strategies are developed already to cut back the signal to noise magnitude relation of the hyperspectral image. However, the stationary noise of the many denoising ways developed cannot be applied on to the gauge boson noise. Thus, the each gauge boson and thermal noise square measure gift within the captured hyperspectral image (HSI). during this paper, we tend to projected a replacement denoising framework known as tensor-based filtering employing a PARAFAC tensor decomposition methodology for scale back each noise. The proposed technique is performs higher in removing noise as compared with different strategies like Multiple linear regression (MLR) algorithm and combined algorithm called multidimensional wavelet transforms with multiway wiener filter (MWPT-MWF) technique. The performance analysis of the new denoising framework has more efficient for reducing signal dependent (PN) and signal independent noise (TN) as compared with other conventional method. Hence this novel denoising approach would be more beneficial for detection of skin allergy and also this algorithm will be very useful for detection of retinal exudates and diagnosis of diabetes mellitus and retinopathy disease in medical application.

Multi-dimensional Legendre wavelets approach on the Black-Scholes and Heston Cox Ingersoll Ross equations

The one dimension Legendre Wavelet is a numerical method to solve one dimension equation. In this paper Black-Scholes equation (B-S), that has applied via single asset American option and Heston Cox- Ingersoll- Ross equation (HCIR), as partial differential equations have been studied in the form of stochastic model at first. The Black-Scholes and Heston Cox- Ingersoll- Ross Stochastic differential equations (SDE) models are converted to partial differential equations with a basic lemma in stochastic differential equation which called Ito lemma including derivatives and integration calculus in stochastic differential equations. Multi-dimensional Legendre wavelets method is based upon the expanded properties of Legendre wavelets from high order that is utilized to reduce these equations in to a system of algebraic equations. In fact the properties of Legendre wavelets are leads to reduce the PDEs problems to solution the ODEs systems. To ability and efficiency of the proposed techniques, numerical results and comparison with the other numerical method named Adomian decomposition method (ADM) for different values of parameters are tabulated and plotted.

О МНОГОМЕРНОМ ПРЕДСТАВЛЕНИИ СИГНАЛОВ АВТОМАТИЧЕСКИХ ДОЗИРУЮЩИХ УСТРОЙСТВ

The article describes the development of a special approach based on using multidimensional wavelet distributions principle to monitor and control the feed dozing processes in the mix preparation unit. As a key component, this approach uses the multidimensional time-frequency Wigner-Ville distribution, which is the part of Cohen's class distributions. The research focuses on signals characterizing mass transfer processes in the form of material flow measuring signals in relevant points of the unit. Wigner-Ville distribution has been shown in time terms as Fourier transform of products of multiplied parts of the signal under consideration for past and future time moments; corresponding distribution for the frequency spectrum is shown as Fourier transform of the products of signal parts for high-frequency and low-frequency fragments of the signal spectrum. It has been noted that when using a complex model of a dozing signal, discrete values (samples) of the latter are considered as its real values. The description of the signal parameters (amplitude, phase, frequency) has been carried out with the help of Hilbert transform. In Cohen's class distributions which represent one-dimensional non-stationary flow signals, the concept of ‘instantaneous frequency’ has been introduced. A graphical explanation for the transformation of a process flow signal from a one-dimensional time domain to a time-frequency 2 D/ 3 D -space is presented. The technology of developing a multidimensional image in the form of Wigner distribution for one-dimensional signals of continuous spiral or screw-type feeders has been examined in detail. There have been considered the features to support Wigner distribution, which allow to guess the presence or absence of time-frequency distribution elements in the interval of signal recording. There has been demonstrated how Wigner distribution can be obtained for a continuous-intermittent feeding signal. It has been concluded that for a certain types of the signal for zero fragments of the latter, non-zero time-frequency elements (i.e. virtual, anomalous ones) appear on the distribution. In addition to Wigner distribution, two other distributions - of Rihachek and Page - are considered. They display the same signal and also contain virtual elements, but in different domains of the time-frequency space. A generalized multidimensional compound signal distribution with a so-called distribution kernel available in it is presented, which includes a correction parameter that allows controlling the intensity of the virtual signal energy.

The radial wavelet frame density estimator

The estimation of probability densities is one of the fundamental problems in scientific research. It has been shown that Wavelet Density Estimators, which are a well-documented nonparametric approach, outperform other nonparametric estimators in problems involving densities with discontinuities and local features. However, the use of this type of estimators is not widely extended in the scientific community mainly because of their heavy computational complexity and their difficult algorithmic implementation. A novel multidimensional Wavelet Density Estimator approach based on new multidimensional scaling functions with analytic closed-form expressions is proposed. The key advantages of the proposed estimator are its simpler multidimensional algorithmic implementation and its significant reduction in computational complexity. Algorithmic formulations for four different data analysis scenarios are presented: (1) batch processing of input data, (2) online estimation for stationary process, (3) online estimation for non-stationary contexts and (4) batch estimation of high-dimensional data. The assessment results show that the proposed approach reduces the computational time of the estimation process while maintaining competitive estimation errors.

Noise Removal Based on Tensor Modelling for Hyperspectral Image Classification

With the current state-of-the-art computer aided manufacturing tools, the spatial resolution of hyperspectral sensors is becoming increasingly higher thus making it easy to obtain much more detailed information of the scene captured. However, the improvement of the spatial resolution also brings new challenging problems to address with signal dependent photon noise being one of them. Unlike the signal independent thermal noise, the variance of photon noise is dependent on the signal, therefore many denoising methods developed for the stationary noise cannot be applied directly to the photon noise. To make things worse, both photon and thermal noise coexist in the captured hyperspectral image (HSI), thus making it more difficult to whiten noise. In this paper, we propose a new denoising framework to cope with signal dependent nonwhite noise (SDNW), Pre-estimate—Whitening—Post-estimate (PWP) loop, to reduce both photon and thermal noise in HSI. Previously, we proposed a method based on multidimensional wavelet packet transform and multi-way Wiener filter which performs both white noise and spectral dimensionality reduction, referred to as MWPT-MWF, which was restricted to white noise. We get inspired from this MWPT-MWF to develop a new iterative method for reducing photon and thermal noise. Firstly, the hyperspectral noise parameters estimation (HYNPE) algorithm is used to estimate the noise parameters, the SD noise is converted to an additive white Gaussian noise by pre-whitening procedure and then the whitened HSI is denoised by the proposed method SDNW-MWPT-MWF. As comparative experiments, the Multiple Linear Regression (MLR) based denoising method and tensor-based Multiway Wiener Filter (MWF) are also used in the denoising framework. An HSI captured by Reflective Optics System Imaging Spectrometer (ROSIS) is used in the experiments and the denoising performances are assessed from various aspects: the noise whitening performance, the Signal-to-Noise Ratio (SNR), and the classification performance. The results on the real-world airborne hyperspectral image HYDICE (Hyperspectral Digital Imagery Collection Experiment) are also presented and analyzed. These experiments show that it is worth taking into account noise signal-dependency hypothesis for processing HYDICE and ROSIS HSIs.

Non-parametric regression for spatially dependent data with wavelets

ABSTRACTWe study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular N-dimensional lattice structure. We show consistency and obtain rates of convergence. The rates are optimal modulo a logarithmic factor in some cases. As an application, we estimate the regression function with multidimensional wavelets which are not necessarily isotropic. We simulate random fields on planar graphs with the concept of concliques (cf. [Kaiser MS, Lahiri SN, Nordman DJ. Goodness of fit tests for a class of markov random field models. Ann Statist. 2012;40:104–130]) in numerical examples of the estimation procedure.

Intelligent control of an MR prosthesis knee using of a hybrid self-organizing fuzzy controller and multidimensional wavelet NN

A Magneto rheological (MR) rotary brake as a prosthesis knee is addressed here. To the gait of the amputee, the brake, automatically adapts knee damping coefficient using only local sensing of the knee torque and position. It is difficult to design a model-based controller, since the MR knee system has nonlinear and very complicated governing mathematical equations. Hence, a Hybrid self-organizing fuzzy controller and multidimensional wavelet neural network (HSFCMWNN) is proposed here to control the knee damping coefficient using of the inverse dynamics of the MR rotary damper. A Self-organizing fuzzy controller (SOFC) is also proposed and during the control process, the SOFC continually updates fuzzy rules, while at the beginning contains blank fuzzy rules. Therefore the problem of finding appropriate fuzzy rules and consequently membership functions for the design of a fuzzy logic controller is ignored by using of the SOFC. It is, however, difficult to select appropriate parameters (learning rate and weighting distribution) in the SOFC which are crucial for control of MR prosthesis knee. To deal with this drawback, a hybrid self-organizing fuzzy and multidimensional wavelet neural network is employed appropriately. The proposed strategy uses a Multidimensional wavelet neural network (MWNN) to adjust these parameters in real time, to achieve to optimal values. First, the MWNN is trained by Stochastic gradient algorithm (SGA) and then to reduce the learning cycle to be needed and the appropriate error, a learning procedure based on the Levenberg-Marquardt (LM) algorithm is adopted intentionally. Simulation results demonstrate that the HSFCMWNN performs better in control performance than that of the SOFC in improving gait of the amputee.