Design Of Wavelet Research Articles

Construction of non-stationary biorthogonal Wavelets based on cardinal Chebyshev B-spline

In this paper, we propose a novel method for designing non-stationary biorthogonal wavelets that leverages Bezout equations to compute wavelet filter coefficients. Our approach integrates cardinal Chebyshev B-splines of varying degrees (second, third, and fourth) as bases for constructing these wavelets, providing explicit formulations for both low-pass and high-pass filters at all levels. By employing this method, we streamline the design process, making it more efficient and accessible while accommodating diverse processing requirements. The utilization of Bezout equations offers a systematic framework for deriving wavelet filter coefficients, enhancing the reproducibility and reliability of the design process. This systematic approach ensures that the resulting wavelets possess desired properties such as vanishing moments, smoothness, and optimal localization. Moreover, by incorporating cardinal Chebyshev B-splines, we can effectively capture intricate signal and image features, addressing challenges encountered in traditional wavelet design methods. Our method not only simplifies the design process but also provides a comprehensive solution by explicitly formulating filters and dual filters across all levels. This comprehensive approach ensures that the resulting wavelets meet the specific demands of applications in signal and image processing, including compression, denoising, and pattern recognition. These advancements hold significant implications for various domains, including information technology, healthcare, and engineering, where efficient and reliable processing techniques are crucial. Moving forward, it is imperative to refine algorithms, assess parameter robustness, and conduct thorough empirical validations across diverse datasets and application scenarios. This will ensure the efficacy and scalability of our proposed method and pave the way for further advancements in non-stationary wavelet design and its applications. By continuously improving and validating our approach, we can foster innovation and enhance practical outcomes in a wide range of fields.

Partial discharge pattern recognition algorithm of overhead covered conductors based on feature optimization and bidirectional LSTM‐GRU

AbstractRecognition of partial discharge (PD) patterns is essential for insulation diagnosis of covered conductors in overhead lines. Current research has not sufficiently addressed the complex background noise in real environments, and most detection methods depend primarily on feature engineering or deep learning, suggesting potential for improvement in accuracy and efficiency. This has led the authors to propose a PD pattern recognition algorithm that integrates feature selection and deep learning. This algorithm incorporates the design of a discrete wavelet denoising function specifically tailored to the characteristics of PD for data preprocessing. It employs Bayesian optimization algorithms and light gradient boosting machines for characterizing corona discharge features. Furthermore, it develops multi‐scale clustering features and phase‐resolved features for feature fusion, and constructs insightful features based on the light gradient boosting machine. Finally, a novel deep learning model is formulated, demonstrating exceptional detection performance for early faults in covered conductors. Experimental results show that this algorithm attains an Matthews correlation coefficient score of 0.814, a 13.2% improvement over the baseline algorithm's 0.719, and a speed increase of 39.18%. The final accuracy amounts to 97.85%. This algorithm demonstrates exceptional performance in detecting early insulation faults in conductors.

Reduced Complexity Approximation and Design of Gaussian Impulse Response Filters and Wavelets

Reduced Complexity Approximation and Design of Gaussian Impulse Response Filters and Wavelets

Existence of uncertainty minimizers for the continuous wavelet transform

AbstractContinuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time‐scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals.

Sandpiper Optimization with a Deep Learning Enabled Fault Diagnosis Model for Complex Industrial Systems

Recently, artificial intelligence (AI)-enabled technologies have been widely employed for complex industrial applications. AI technologies can be utilized to improve efficiency and reduce human labor in industrial applications. At the same time, fault diagnosis (FD) and detection in rotating machinery (RM) becomes a hot research field to assure safety and product quality. Numerous studies based on statistical, machine learning (ML), and mathematical models have been available in the literature for automated fault diagnosis. From this perspective, this study presents a novel sandpiper optimization with an artificial-intelligence-enabled fault diagnosis (SPOAI-FD) technique for intelligent industrial applications. The aim is to detect the existence of faults in machineries. The proposed model involves the design of a continuous wavelet transform (CWT)-based pre-processing approach, which transforms the raw vibration signal into a useful format. In addition, a bidirectional long short-term memory (BLSTM) model is applied as a classifier, and the Faster SqueezeNet model is applied as a feature extractor. In order to modify the hyperparameter values of the BLSTM model, the sandpiper optimization algorithm (SPOA) can be utilized, showing the novelty of the work. A wide range of simulation analyses were conducted on benchmark datasets, and the results highlighted the supremacy of the SPOAI-FD algorithm over recent approaches.

New Design of Wavelets Based on the Convolution of Compactly Supported Functions with a Rectangular Pulse

New Design of Wavelets Based on the Convolution of Compactly Supported Functions with a Rectangular Pulse

Design of Biorthogonal Wavelets based on Spline and Spline-like Functions for Image Compression

Wavelet theory inspired from Fourier analysis is based on the basis function and its properties. Different wavelets use different basis functions which may better suit to some applications. The properties of basis functions along with their shape and magnification effects the performance of an application. The standard biorthogonal wavelets utilize spline functions for their construction. In this paper first the design procedure of biorthogonal wavelets is presented. Then a modified spline function is proposed. Based on the proposed spline function, three biorthogonal wavelets are designed with different length. The performance of proposed wavelets is analyzed by applying them on to images for SPIHT compression. The simulation results shown that the proposed wavelets have performed well compared to that of standard spline based biorthogonal wavelets.

Design and Implementation of New Biorthogonal Wavelets and its Application to Image Processing

Wavelet transformation has been an interesting field since its exposure with wavelet-based compression standard embedded zerotree wavelet. Though, the origin of wavelets back to many decades, the presence of research at the very beginning of wavelet bases is also being carried out in the research community. This is because of the wide presence of its applicability as well as its structure of adapting to the type of problem at hand. In this paper, an approach of designing biorthogonal wavelets is presented. This approach may be extended to design variety of wavelets. This paper mainly focus on the design steps and corresponding coding in MATLAB. By varying the length, type of the bases and other parameters, different wavelets may be devised.

A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities

As a general and rigid mathematical tool, wavelet theory has found many applications and is constantly developing. This article reviews the development history of wavelet theory, from the construction method to the discussion of wavelet properties. Then it focuses on the design and expansion of wavelet transform. The main models and algorithms of wavelet transform are discussed. The construction of rational wavelet transform (RWT) is provided by examples emphasizing the advantages of RWT over traditional wavelet transform through a review of the literature. The combination of wavelet theory and neural networks is one of the key points of the review. The review covers the evolution of Wavelet Neural Network (WNN), the system architecture and algorithm implementation. The review of the literature indicates the advantages and a clear trend of fast development inWNNthat can be combined with existing neural network algorithms. This article also introduces the categories of wavelet-based applications. The advantages of wavelet analysis are summarized in terms of application scenarios with a comparison of results. Through the review, new research challenges and gaps have been clarified, which will serve as a guide for potential wavelet-based applications and new system designs.

Adaptive Real-Time Wavelet Denoising Architecture Based on Feedback Control Loop

The discrete wavelet transform is commonly used as a denoising step for many applications, like biomedical applications which are usually suffering from low SNR of the recorded signal. However, the choice of appropriate threshold value for DWT coefficients plays significant role in reconstructing the denoised signal. This paper presents a design of real-time wavelet denoising architecture which is suitable for wide range of real-time denoising applications. In this design, an adaptive thresholding approach based on feedback control loop is proposed to make the architecture more applicable for real-time wavelet denoising. This thresholding method considers a noise level estimator module based on first detail coefficients level 𝑑1 to calculate the unknown standard deviation of background noise. The proposed architecture is developed using MATLAB to simulate the suggested denoising method. The performance of the proposed denoising method is studied in terms of integral gain 𝐺 of feedback control and window size 𝑀 with respect to the improvement in SNR and settling time. The results imply that the proposed denoising architecture is suitable for real-time denoising applications with acceptable improvement in SNR approximately 8 dB.

Heuristic computational design of Morlet wavelet for solving the higher order singular nonlinear differential equations

The aim of this study is to present the numerical solutions of the higher order singular nonlinear differential equations using an advanced intelligent computational approach by manipulating the Morlet wavelet (MW) neural networks (NNs), global approach as genetic algorithm (GA) and quick local search approach as interior-point method (IPM), i.e., GA-IPM. MWNNs is applied to discretize the higher order singular nonlinear differential equations to express the activation function using the mean square error. The performance of the designed MWNNs using the GA-IPM is observed to solve three different variants based on the higher order singular nonlinear differential model to check the significance, efficacy and consistency of the designed MWNNs using the GA-IPM. Furthermore, statistical performances are provided to check the precision, accuracy and convergence of the present approach.

Lifting scheme‐based matched wavelet design for effective characterisation of different types of voltage sag

This study presents a novel scheme for designing biorthogonal wavelets matched to the voltage sag (VS) signals. Instead of using standard wavelets, matched wavelets designed in this study can extract more distinguishing features for better characterisation of sag signals, although this study proposes only the designing process of matched wavelets. The key method used for designing matched wavelets is the lifting scheme, which has never been reported in the literature for constructing matched wavelets for PQ signals. Besides using the lifting scheme, the proposed work preprocesses sag signals to make input signal of lifting scheme rich of sag-related information. During pre-processing, 1-D sag signal is first converted to 2-D form for capturing information of every small transition (which may be overlooked in 1-D form) and then made 1-D by ring projection to implement 1-D lifting scheme. In this way, biorthogonal wavelets have been well matched to every type of VS signal collected through the experimental setup simulating different line faults, induction motor starting, transformer energisation and heavy load starting. Also, the characteristics of designed wavelets are evaluated in a MATLAB environment using frequency response and pole-zero mapping in z-plane. Higher PSNR values during signal reconstruction proved outperformance of newly designed matched wavelets.

Discrete Wavelet Design for Bearing Fault Diagnosis Using Particle Swarm Optimization

Rolling bearings are widely used in a large variety of industrial applications. Therefore, it is necessary to provide an efficient fault detection and diagnosis mechanism to prevent component failure and poor performance during operation. This paper proposes a novel classification scheme based on the design of discrete wavelets best adapted to vibration signal analysis in order to identify and properly classify rolling bearing defects. Through polyphase representation of the wavelet filter bank, and using the particle swarm optimization (PSO) algorithm, the appropriate discrete wavelet associated filters are optimized to achieve the best fault classification accuracy. Simulation results show that the proposed wavelet design approach outperforms the well-known standard wavelets regardless the employed classifier and leads to an average fault classification improvement of about 2%.

Design of nonstationary wavelets through the positive solution of Bezout’s equation

In this paper, we present a new technique for constructing a nonstationary wavelet. The key idea relies on the following: for each wavelet level, we solve the Bezout’s equation and we propose a positive solution over the interval [–1, 1]. Using the Bernstein’s polynomials we approximate this proposed positive solution with the intention to perform a spectral factorization.

Novel design of a fractional wavelet and its application to image denoising

This paper proposes a new wavelet family based on fractional calculus. The Haar wavelet is extended to fractional order by a generalization of the associated conventional low-pass filter using the fractional delay operator Z-D. The high-pass fractional filter is then designed by a simple modulation of the low-pass filter. In contrast, the scaling and wavelet functions are constructed using the cascade Daubechies algorithm. The regularity and orthogonality of the obtained wavelet basis are ensured by a good choice of the fractional filter coefficients. An application example is presented to illustrate the effectiveness of the proposed method. Thanks to the flexibility of the fractional filters, the proposed approach provides better performance in term of image denoising.

Design of analytic wavelet transform with optimal filter coefficients for cancer diagnosis using genomic signals

DNA sequence analysis and gene expression analysis through genomic signal processing played an important role in cancer diagnosis in recent years. Cancer diagnosis through gene expression data, discrete Fourier transform, discrete wavelet transform (DWT) and IIR low pass filter are frequently used but suffer from drawbacks like longer essential time-support. Analytic wavelet transform with optimal filter coefficients for cancer diagnosis using genomic signals is designed in this paper. The proposed technique consists of three modules namely, pre-processing module, optimisation module and transform and cancer diagnosis module. Initially, the filter coefficients are optimally found out using group search optimiser. Then, the optimal coefficients and the pre-processed DNA sequence is applied to analytic wavelet transform and subsequently, diagnosis for the cancer cell is made based on the threshold. DNA sequences obtained from National Centre for Biotechnology Information (NCBI) forms the database for the evaluation. Evaluation metrics parameters employed are sensitivity, specificity and accuracy. Comparison is made to the base method and analytic transform technique for more analysis. From the results, we can observe that the proposed technique has achieved good results attaining accuracy of 91.6% which is better than other compared techniques.

An Approximate Low-Power Lifting Scheme Using Reversible Logic

Haar Wavelet transform is an efficacious class of wavelet transform that satisfies both symmetry and orthogonality properties which are crucial in handling boundary distortion and energy preservation in image processing applications. Such applications demand power efficient design solutions that deliver high performance. Reversible logic has emerged as a solution that incorporates logical and physical reversibility to realise low power designs. This paper presents a reversible logic based design of Haar wavelet transform and lifting scheme for Haar wavelet transform, a first in literature of reversible logic. The designs are analysed to measure the efficiency of reversible logic implementations in terms of Quantum Cost (QC), Constant Inputs (CI), Garbage Outputs (GO) and Gate Count (GC). Furthermore, this paper proposes two architectures for Reversible Approximate Full Adder (RAFA) - RAFA-1 and RAFA-2; optimised explicitly for reversible logic based implementation. The proposed architectures have 25% Error Rate (ER) and optimised QC, CI, GC and GO when compared to existing exact and approximate full adder architectures implemented using reversible logic. Functional verification of the proposed architectures are performed on FPGA using $512 \times 512$ image. The efficiency of the image processing application is projected in terms of Structural Similarity Index Measure (SSIM) and Peak Signal to Noise Ratio (PSNR). Average SSIM and average PSNR are found to be 0.9679 and 31.81dB for RAFA-1 and 0.9696 and 32.15dB for RAFA-2 which are comparable with exact full adder based design.

Design of analytic wavelet transform with optimal filter coefficients for cancer diagnosis using genomic signals

DNA sequence analysis and gene expression analysis through genomic signal processing played an important role in cancer diagnosis in recent years. Cancer diagnosis through gene expression data, discrete Fourier transform, discrete wavelet transform (DWT) and IIR low pass filter are frequently used but suffer from drawbacks like longer essential time-support. Analytic wavelet transform with optimal filter coefficients for cancer diagnosis using genomic signals is designed in this paper. The proposed technique consists of three modules namely, pre-processing module, optimisation module and transform and cancer diagnosis module. Initially, the filter coefficients are optimally found out using group search optimiser. Then, the optimal coefficients and the pre-processed DNA sequence is applied to analytic wavelet transform and subsequently, diagnosis for the cancer cell is made based on the threshold. DNA sequences obtained from National Centre for Biotechnology Information (NCBI) forms the database for the evaluation. Evaluation metrics parameters employed are sensitivity, specificity and accuracy. Comparison is made to the base method and analytic transform technique for more analysis. From the results, we can observe that the proposed technique has achieved good results attaining accuracy of 91.6% which is better than other compared techniques.

An intelligent learning approach for improving ECG signal classification and arrhythmia analysis.

The recognition of cardiac arrhythmia in minimal time is important to prevent sudden and untimely deaths. The proposed work includes a complete framework for analyzing the Electrocardiogram (ECG) signal. The three phases of analysis include 1) the ECG signal quality enhancement through noise suppression by a dedicated filter combination; 2) the feature extraction by a devoted wavelet design and 3) a proposed hidden Markov model (HMM) for cardiac arrhythmia classification into Normal (N), Right Bundle Branch Block (RBBB), Left Bundle Branch Block (LBBB), Premature Ventricular Contraction (PVC) and Atrial Premature Contraction (APC). The main features extracted in the proposed work are minimum, maximum, mean, standard deviation, and median. The experiments were conducted on forty-five ECG records in MIT BIH arrhythmia database and in MIT BIH noise stress test database. The proposed model has an overall accuracy of 99.7 % with a sensitivity of 99.7 % and a positive predictive value of 100 %. The detection error rate for the proposed model is 0.0004. This paper also includes a study of the cardiac arrhythmia recognition using an IoMT (Internet of Medical Things) approach.

Memory Efficient High Speed Systolic Array Architecture Design with Multiplexed Distributed Arithmetic for 2D DTCWT Computation on FPGA

This paper presents customized Systolic Array Architecture (SAA) design of Dual Tree Complex Wavelet (DTCWT) sub band computation based on multiplexed Distributive Arithmetic Algorithm (DAA). The proposed architecture is memory efficient and operates at frequencies greater than 300 MHz in decomposing 256 x 256 input images. Three architectures such as reduced order structure, multiplexed DA structure and zero pad structure are designed and evaluated for its performances for DTCWT computation minimizing arithmetic operations with improved latency. The proposed design is modeled in Verilog HDL and is implemented on Spartan-6 and Virtex-5 FPGA considering Xilinx ISE FPGA design flow. The latency of proposed architectures is evaluated to be 15 clock cycles and throughput is estimated to be 4 outputs for every 5 clock cycles. The SAA architecture occupies less than 12% of FPGA resources and consumes less than 10 mW of power on FPGA platform.