Fast Discrete Wavelet Transform Research Articles

Two-Dimensional Damage Localization Using a Piezoelectric Smart Aggregate Approach-Implementation on Arbitrary Shaped Concrete Plates.

This paper presents the application of a hybrid approach for damage localization in concrete plates of arbitrary geometric shapes and a constant thickness. The hybrid algorithm utilizes fast discrete wavelet transformation, energy approach and time of flight criteria for the purpose of the localization of single- and multi-damage problems inside or on the periphery of concrete plates. A brief theoretical background of the hybrid method as well as numerical procedures for modeling the piezoelectric smart aggregate and ultrasonic wave propagation are presented. Experimental and numerical verification of the damage localization were performed on square samples/models with one or two damages and with 16 positions of piezoelectric smart actuator/sensor aggregates. After the verification of the hybrid method, a numerical simulation was performed on models with one or two damages for plates of arbitrary geometric shapes. Based on the obtained results, it was concluded that the proposed method can be applied to damage localization in concrete plates of arbitrary geometric shapes. The presented method and numerical procedure can be further used in research through varying the geometry, number and position of damages as well as the number and position of piezoelectric smart aggregates.

Dynamic and explainable deep learning-based risk prediction on adjacent building induced by deep excavation

Since deep excavation will inevitably generate great disturbances in the surrounding environment, excessive vertical displacement of adjacent buildings is one of the crucial concerns in ensuring excavation safety. Therefore, this study proposes a hybrid deep learning model called Att-Bilstm under the integration of the bidirectional long and short-term memory neural network (Bi-LSTM) and the self-attention mechanism, aiming to dynamically and accurately predict the upcoming excavation-induced risk to adjacent buildings. To better improve the explanation of the Att-Bilstm model, the Shapley Additive explanations (SHAP) analysis is conducted to measure the contribution of variables in risk prediction, while the Latin hypercube sampling (LHS) approach is employed to assess risk evolution. The developed deep learning approach is verified in a case study about the excavation of Area A of the Jing'an Temple Station on Shanghai Metro Line 14. Results indicate that: (1) The data denoising technique fast discrete wavelet transform (FDWT) and the automatic hyperparameter tunning method Bayesian optimization are beneficial to establish a highly accurate Att-Bilstm predictor with the proper time sliding window, reaching the MAPE smaller than 0.062. (2) Variables identified as having a greater influence through SHAP analysis require increased attention for effective control of excavation-induced risks. The simulation-based approach provides early risk warnings, contributing to risk mitigation in the uncertain and dynamic underground environment. (3) Compared to three other popular deep learning models, Att-Bilstm exhibits greater robustness in handling different levels of incomplete monitoring data, achieving a MAPE lower than 0.070 even with 60% missing data. In short, this study contributes to the dynamic perception and understanding of potential excavation-induced risks to adjacent buildings, significantly enhancing the reliability of risk mitigation decisions.

Fully learnable deep wavelet transform for unsupervised monitoring of high-frequency time series

High-frequency (HF) signals are ubiquitous in the industrial world and are of great use for monitoring of industrial assets. Most deep-learning tools are designed for inputs of fixed and/or very limited size and many successful applications of deep learning to the industrial context use as inputs extracted features, which are a manually and often arduously obtained compact representation of the original signal. In this paper, we propose a fully unsupervised deep-learning framework that is able to extract a meaningful and sparse representation of raw HF signals. We embed in our architecture important properties of the fast discrete wavelet transform (FDWT) such as 1) the cascade algorithm; 2) the conjugate quadrature filter property that links together the wavelet, the scaling, and transposed filter functions; and 3) the coefficient denoising. Using deep learning, we make this architecture fully learnable: Both the wavelet bases and the wavelet coefficient denoising become learnable. To achieve this objective, we propose an activation function that performs a learnable hard thresholding of the wavelet coefficients. With our framework, the denoising FDWT becomes a fully learnable unsupervised tool that does not require any type of pre- or postprocessing or any prior knowledge on wavelet transform. We demonstrate the benefits of embedding all these properties on three machine-learning tasks performed on open-source sound datasets. We perform an ablation study of the impact of each property on the performance of the architecture, achieve results well above baseline, and outperform other state-of-the-art methods.

Fast Discrete Wavelet Transformation Using FPGAs and Distributed Arithmetic

ABSTRACT The discrete wavelet transform has gained the reputation of being a very effective signal analysis tool for many practical applications. However, due to its computation-intensive nature, current implementations of the transform fall short of meeting real-time processing requirements of most applications. This paper describes a parallel implementation of the discrete wavelet transform and its inverse using high-density field programmable logic devices (FPGAs). The implementation exploits the lookup table-based architecture of Virtex FPGAs, by reformulating the wavelet computation in accordance with the distributed arithmetic algorithm. Performance results show that the distributed arithmetic formulation results in a considerable performance gain compared with the conventional arithmetic formulation of the wavelet computation. Finally, we show that the FPGA implementation outperforms alternative software implementations of the discrete wavelet transform.

Automated atrophy assessment for Alzheimer's disease diagnosis from brain MRI images

An inventive scheme for automated tissue segmentation and classification is offered in this paper using Fast Discrete Wavelet Transform (DWT)/Band Expansion Process (BEP), Kernel-based least squares Support Vector Machine (KLS-SVM) and F-score, backed by Principal Component Analysis (PCA). Using input as T1, T2 and Proton Density (PD) scans of patients, CSF (Cerebrospinal Fluid), WM (White matter) and GM (Gray matter) are afforded as output, which act as hallmark for brain atrophy and thus sustaining in diagnosis of Alzheimer's disease (AD) from Mild Cognitive Impairment (MCI) and Healthy Controls (HC). The blending of BEP features from DWT and texture features from Gray Level Co-occurrence Matrix (GLC) promises to be a savior in atrophy revelation of the segmented tissues. Data used for evaluation of this study is taken from the ADNI database that encloses T1-weighted s-MRI (Structural Magnetic Imaging Resonance) scans of 158 patients with AD and 145 HC. Preprocessing steps unearthed five parameters for classification (i.e. cortical thickness, curvature, gray matter volume, surface area, and sulcal depth), in the preliminary step. For challenging the classifier performance, ROC (Receiver operating characteristics) curves are painted and the SVM classifiers of two-dimensional spaces took the top two important features as classification features for separating HC and AD to the maximum extent. The final results revealed that Fast DWT + F-Score + PCA + KLS-SVM + Poly Kernel is giving 100% tissue classification accuracy for test samples under consideration with only 7 input features.

A Fast Adaptive Wavelet Scheme in RBF Collocation for Nearly Singular Potential PDEs

We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast Discrete Wavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the proposed adaptive scheme can detect the singularities both in the domain and near the boundaries. Moreover, the proposed adaptive scheme can be utilized for capturing the regions with high gradient both in the solution and its spatial derivatives. Due to the simplicity of the proposed method, it can be efficiently applied to large scale nearly singular engineering problems.

GPU Computing based fast discrete wavelet transform for l1-regularized SPIRiT reconstruction

ABSTRACTParallel imaging is a technique to shorten the acquisition time by reducing the data size in phase encoding direction. Compressed Sensing is a technique to improve the performance of parallel imaging based reconstruction methods such as l1-regularized SPIRiT by adding the regularization term, which leads to frequent calculations of Discrete Wavelet Transform (DWT) with high time cost. However, clinical practice of MRI scan requires fast or real-time reconstruction with high image quality. In this paper, by taking advantage of the properties of parallel imaging and GPU computing, we develop a fast three-dimensional DWT for parallel imaging based reconstruction methods such as l1-regularized SPIRiT. Computational results show that fast DWT in l1-regularized SPIRiT MRI reconstruction is approximately three times faster than the conventional DWT. Computational results also show that fast DWT for reconstructing an 80 × 150 × 32 × 80 Cardiac MRI dataset by l1-regularized SPIRiT is approximately 20 per cent faster than l1-regularized SPIRiT of the conventional DWT.

Characteristic of decorrelation properties of spline wavelet transformation

This article is devoted to the application of spline wavelet transformation to sequences of strongly correlated random variables. The method of data processing using spline wavelets allows to weaken their correlations, which was shown in earlier published works [1, 2]. There have also been researches that prove the effectiveness of the using linear discrete wavelet transformation (DWT) to sequences of random variables based on the real data from the issues of the mass service theory. In this article, we explore the effectiveness of using a quadratic fast DWT, formulate the corresponding theorem and show the result of numerical experiments.

An Automated and Intelligent Medical Decision Support System for Brain MRI Scans Classification.

A wide interest has been observed in the medical health care applications that interpret neuroimaging scans by machine learning systems. This research proposes an intelligent, automatic, accurate, and robust classification technique to classify the human brain magnetic resonance image (MRI) as normal or abnormal, to cater down the human error during identifying the diseases in brain MRIs. In this study, fast discrete wavelet transform (DWT), principal component analysis (PCA), and least squares support vector machine (LS-SVM) are used as basic components. Firstly, fast DWT is employed to extract the salient features of brain MRI, followed by PCA, which reduces the dimensions of the features. These reduced feature vectors also shrink the memory storage consumption by 99.5%. At last, an advanced classification technique based on LS-SVM is applied to brain MR image classification using reduced features. For improving the efficiency, LS-SVM is used with non-linear radial basis function (RBF) kernel. The proposed algorithm intelligently determines the optimized values of the hyper-parameters of the RBF kernel and also applied k-fold stratified cross validation to enhance the generalization of the system. The method was tested by 340 patients’ benchmark datasets of T1-weighted and T2-weighted scans. From the analysis of experimental results and performance comparisons, it is observed that the proposed medical decision support system outperformed all other modern classifiers and achieves 100% accuracy rate (specificity/sensitivity 100%/100%). Furthermore, in terms of computation time, the proposed technique is significantly faster than the recent well-known methods, and it improves the efficiency by 71%, 3%, and 4% on feature extraction stage, feature reduction stage, and classification stage, respectively. These results indicate that the proposed well-trained machine learning system has the potential to make accurate predictions about brain abnormalities from the individual subjects, therefore, it can be used as a significant tool in clinical practice.

Medical Image Fusion using Fast Discrete Wavelet Transform and Quality Assessment of Fused Images

Medical Image Fusion using Fast Discrete Wavelet Transform and Quality Assessment of Fused Images

Novel Implementation of Recursive Discrete Wavelet Transform for Real Time Computation with Multicore Systems on Chip (SOC)

The discrete wavelet Transform (DWT) has been studied and developed in various scientific and engineering fields. Its multi-resolution and locality nature facilitates application required for progressiveness in capturing high-frequency details. However, when dealing with enormous data volume, the performance may drastically reduce. The multi-resolution sub-band encoding provided by DWT enables for higher compression ratios, and progressive transformation of signals. The widespread usage of the DWT has motivated the development of fast DWT algorithms and their tuning on all sorts of computer systems. However, this transformation comes at the expense of additional computational complexity. Achieving real-time or interactive compression/de-compression speed, therefore, requires a fast implementation of DWT that leverages emerging parallel hardware systems. The recent advancement in the consumer level multicore hardware is equipped with Single Instruction and Multiple Data (SIMD) power.In this study, Parallel Discrete Wavelet Transform has been developed with novel Adaptive Load Balancing Algorithm (ALBA). The DWT is parallelized, partitioned, mapped and scheduled on single core and Multicore. The Parallel DWT is developed in C# for single and Intel Quad cores as well as the combination of C and CUDA is implemented on GPU. This brings the significant performance on a consumer level PC without extra cost.

Texture Classification for Liver Tissues from Ultrasonic B-Scan Images Using Testified PNN

Visual criteria for diagnosing liver diseases, such as cirrhosis, from ultrasound images can be assisted by computerized texture classification. This paper proposes a system applying a PNN (Pyramid Neural Network) for classifying the hepatic parenchymal diseases in ultrasonic B-scan texture. In this study, we propose a multifractal-dimensions method to select the patterns for the training set and the validation sets. A modified box-counting algorithm is used to calculate the dimensions of the B-scan images. FDWT (Fast Discrete Wavelet Transform) is applied for feature extraction during the preprocessing. The structure of the proposed neural network is testified by training and validation sets by cross-validation method. The performance of the proposed system and a system based on the conventional multilayer network architecture is compared. The results show that, compared with the conventional 3-layer neural network, the performance of the proposed pyramid neural network is improved by efficiently utilizing the lower layer of the neural network.

CLASSIFICATION OF CIRRHOSIS FROM B-SCAN IMAGES USING PYRAMID NEURAL NETWORK

This paper proposes a system applying a pyramid neural network for classifying the hepatic parenchymal diseases in ultrasonic B-scan texture. The conventional multilayer neural network emphasizing on the data carried by the last hidden layer has the drawback of not fully utilizing the information carried by the input data. A pyramid network can solve the problem successfully. To solve the common problem of neural network, which is time-consuming in computation, FDWT (Fast Discrete Wavelet Transform) is a key technique used during preprocessing to cut down the size of patterns feed to the network. The B-scan patterns are wavelet transformed, and then the compressed data is fed into a pyramid neural network to diagnose the type of cirrhotic diseases. The performance of the proposed system and that of a system based on the conventional multilayer network architecture is compared. The result shows that compared to the conventional 3-layer neural network, the performance of the proposed pyramid neural network is improved by effectively utilizing the lower layer of the neural network.

An Algebraic Structure of Orthogonal Wavelet Space

In this paper we study the algebraic structure of the space of compactly supported orthonormal wavelets over real numbers. Based on the parameterization of wavelet space, one can define a parameter mapping from the wavelet space of rank 2 (or 2-band, scale factor of 2) and genus gto the ( g−1) dimensional real torus (the products of unit circles). By the uniqueness and exactness of factorization, this mapping is well defined and one-to-one. Thus we can equip the rank 2 orthogonal wavelet space with an algebraic structure of the torus. Because of the degenerate phenomenon of the paraunitary matrix, the parameterization map is not onto. However, there exists an onto mapping from the torus to the closure of the wavelet space. And with such mapping, a more complete parameterization is obtained. By utilizing the factorization theory, we present a fast implementation of discrete wavelet transform (DWT). In general, the computational complexity of a rank morthogonal DWT is O( m 2 g). In this paper we start with a given scaling filter and construct additional ( m−1) wavelet filters so that the DWT can be implemented in O( mg). With a fixed scaling filter, the approximation order, the orthogonality, and the smoothness remain unchanged; thus our fast DWT implementation is quite general.

Methods of radar data compression and target identification based on biorthogonal FDWT

In this paper, by using the biorthogonal quadrature filters, the biorthogonal multiresolution analysis of finite dimension space equipped with inner product and the fast discrete wavelet transform (FDWT) are constructed. The dual transform method is proposed and the radar data storage is reduced by it. The method of choosing the wavelet coefficients, and the methods of correlation and nearest neighbor classification in wavelet domain based on the compressed data, are presented. The experimental results of the classification, using the high resolution range returns from six kinds of aircrafts, show that the methods of transform, compression and recognition are efficient.

Cubic Spline Wavelet Bases of Sobolev Spaces and Multilevel Interpolation

In this paper, a semi-orthogonal cubic spline wavelet basis of homogeneous Sobolev spaceH20(I) is constructed, which turns out to be a basis of the continuous spaceC0(I). At the same time, the orthogonal projections on the wavelet subspaces inH20(I) are extended to the interpolating operators on the corresponding wavelet subspaces inC0(I). A fast discrete wavelet transform (FWT) for functions inC0(I) is also given, which is different from the pyramid algorithm and easy to perform using a parallel algorithm. Finally, it is shown that the singularities of a function can be traced from its wavelet coefficients, which provide an adaptive approximation scheme allowing us to reduce the operation time in computation.