Daubechies Filters Research Articles

Wavelet-Based precipitation preprocessing for improved drought Forecasting: A Machine learning approach using tunable Q-factor wavelet transform and maximal overlap discrete wavelet transform

Drought forecasting plays a crucial role in mitigating the severe agricultural and social consequences caused by droughts. The fluctuating nature of droughts makes it difficult to develop an effective drought forecasting model without preprocessing the input data. This paper proposes a novel approach that introduces the tunable Q-factor wavelet transform (TQWT) with the maximal overlap discrete wavelet transform (MODWT) based Fejér–Korovkin, Coiflet, and Daubechies filters in the decomposition of precipitation data for the extended lead time forecasting of the standardized precipitation evapotranspiration index (SPEI). The decomposed datasets have been coupled with Matern Gaussian process regression (MGPR), exponential Gaussian process regression (EGPR), linear support vector machine (LSVM), and coarse Gaussian support vector machine (CGSVM), and formed hybrid models to forecast SPEI-12 and SPEI-18 for several lead times (i.e., 6, 12, 18, and 24 months). Results of the study represent that the wavelet-based hybrid models are capable of predicting SPEI-12 and SPEI-18 effectively for different lead times with promising results. Both TQWT and MODWT coupled with MGPR yielded reasonable performances for the lead time of 6 months in all stations. However, for the higher lead times, TQWT coupled with MGPR outperformed other hybrid models. The results of the TQWT-MGPR for SPEI-12 are more effective than SPEI-18 in different lead times. The study highlights that preprocessing of precipitation data using TQWT is a promising direction for drought forecasting, and the findings obtained from drought forecasting can be utilized in the areas of water and agricultural resource management to effectively mitigate and alleviate the potential impacts of future droughts.

Advanced detection of cardiac arrhythmias using a three-stage CBD filter and a multi-scale approach in a combined deep learning model

In this paper, we present a new method based on deep learning for the detection of cardiac arrhythmias. The proposed method is based on three fundamental components: an inception-ResNet structure, bidirectional LSTM layers and a multi-scale signal analysis technique. To improve processing of the MIT-BIH arrhythmia dataset, we have developed a three-stage CBD filter that successively incorporates Chebyshev, Butterworth and Daubechies filters. This filter is designed meticulously to denoise the ECG signal while preserving its relevant features. By combining this filter with our deep learning model and multi-scale approach, we have significantly improved the quality of the ECG signal. Such integration not only enhances the accuracy and reliability of arrhythmia detection, but also contributes to the identification of complex patterns in various temporal and spatial dimensions. In terms of performance, our model is remarkably robust, with 98.94% accuracy and 97.20% precision.

Method for Adaptive Wavelet Filtering of Speech Signals Based on Daubechies Filters with Minimization of Errors in Finding Optimal Thresholds

The paper deals with the problem of adaptive wavelet filtering of speech signals based on Daubechies filters with minimization of errors in finding optimal threshold values. This approach is similar to estimating a speech signal by averaging it using a kernel that is locally adapted to the smoothness of the signal. In this case, a set of coupled mirror filters decomposes the speech signal in a discrete domain according to the orthogonal Daubechies wavelet basis into several frequency bands. Noise removal of speech signals is performed as a complete cutoff of the wavelet transform coefficients based on the assumption that their small amplitude values are noise. Thus, in the Daubechies wavelet basis, where coefficients with large amplitude correspond to abrupt changes in the speech signal, such processing preserves only the intermittent components originating from the input speech signal without adding other components caused by noise. In general, by equating small coefficients to zero, we perform adaptive smoothing that depends on the smoothness of the input speech signal. By keeping the coefficients of large amplitude, we avoid smoothing out sharp drops and preserve local features. Performing this procedure on several scales leads to a gradual reduction of the noise effect on both piecewise smooth and discontinuous parts of the speech signal. In view of this, the main task of the study is to adaptively generate micro-local thresholds, which will reduce the impact of additive noise on the pure form of the speech signal, and preserve significant wavelet coefficients of large amplitude that characterize the local features of the speech signal. Thus, as a result of our work, we have proved the feasibility of developing the presented method of wavelet filtering of speech signals with adaptive thresholds based on Daubechies wavelet analysis, which minimizes the loss of speech intelligibility and allows for noise removal depending on the properties and physical nature of the processed data.

Use of Paraconsistent Feature Engineering to support the Long Term Feature choice for Speaker Verification

The state-of-art models for speech synthesis and voice conversion can generate synthetic speech perceptually indistinguishable from human speech, and speaker verification is crucial to prevent breaches. The building feature that best distinguishes genuine speech between spoof attacks is an open research subject. We used the baseline ASVSpoof2017, Transfer Learning (TL) set, and Symlet and Daubechies Discrete Wavelet Packet Transform (DWPT) for this investigation. To qualitatively assess the features, we used Paraconsistent Feature Engineering (PFE). Our experiments pointed out that for the use of more robust classifiers, the best choice would be the AlexNet method, while in terms of classification regarding the Equal Error Rate metric, the best suggestion would be Daubechies filter support 21. Finally, our findings indicate that Symlet filter support 17 as the most promising feature, which is evidence that PFE is a useful tool and contributes to feature selection.

Forecasting Philippine Household Final Consumption Expenditure on Education Using Discrete Wavelet Transformation on Hybrid ARIMA-ANN Model

Objective: This study conveys a forecast of household final consumption expenditure in education of the Philippines from 1st quarter and 4th quarter of 2023. Methods/Analysis: The household final consumption expenditure in education data was obtained from the Philippine Statistics Authority which was part of the National Report for the 1st quarter of 1998 up to the 4th quarter of 2018. The data were forecasted using ARIMA, ANN, Hybrid ARIMA - ANN, and the proposed Discrete Wavelet Transformation using Daubechies filter on the Hybrid ARIMA - ANN. Findings: The forecasting accuracy of the model for a 1 year and 5 year forecast was compared with ARIMA, ANN, and Hybrid ARIMA - ANN through the value of its individual Mean Squared Error, Root Mean Squared Error, and Mean Absolute Percentage Error. It was shown that the proposed DWT using Daubechies filter on Hybrid ARIMA-ANN has an MSE of 0.0009, RMSE of 0.0304, and MAPE of 0.1750 for 1 year forecast and an MSE of 0.0004, RMSE of 0.0194, and MAPE of 0.1167 for the 5 year forecast. It was revealed that the proposed model has the best forecasting performance comparing to ARIMA, ANN, and Hybrid ARIMA - ANN. Novelty/ Improvement: For the Department of Education of the Philippines, preparations and plans can be develop to cope up with the forecasted expenditure on education. For the citizen, the result of this research will give awareness on the movement of expenses in education and will let them prepare for it. Other forecasting models and filters on DWT can be utilized on future works which may improve the results of this study. Keywords: Daubechies Filter, Discrete Wavelet Transformation, Education, Household Expenditure, Hybrid ARIMA-ANN, Time Series Forecasting

Optimasi Keamanan Watermarking pada Daubechies Transform Berbasis Arnold Cat Map

Digital image security using Transform Domain algorithms such as Discrete Wavelet Transform (DWT) has been widely used. To improve the security of the DWT algorithm needs to randomize the pixel coefficient, namely Arnold Cat Map (ACM). Computing ACM as one of the chaos functions is known to be fast and fits with Transform Domain. DWT has been implemented in the Daubechies filter which is the development of the Haar filer. In this paper, we proposed the message insertion model using a combination of DWT and ACM on a 512x512 piskel grayscale image and a 64x64 pixel message on the LL subband. The experiments were performed on 2 different images to determine the ability produced by the combined algroithm. The ability test for message insertion process is done through Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR) and comparation between original image histogram and image insertion histogram. While in the process of message extraction, algorithmic capability test is done by calculating Normalized Cross Correlation (NCC) and its correlation. The highest MSE result is 2.9502 and the highest PSNR is 43.4323 dB, while the NCC value is 237.3584 with correlation 0.7181.

A Comparative Study of Two State-of-the-Art Feature Selection Algorithms for Texture-Based Pixel-Labeling Task of Ancient Documents

Recently, texture features have been widely used for historical document image analysis. However, few studies have focused exclusively on feature selection algorithms for historical document image analysis. Indeed, an important need has emerged to use a feature selection algorithm in data mining and machine learning tasks, since it helps to reduce the data dimensionality and to increase the algorithm performance such as a pixel classification algorithm. Therefore, in this paper we propose a comparative study of two conventional feature selection algorithms, genetic algorithm and ReliefF algorithm, using a classical pixel-labeling scheme based on analyzing and selecting texture features. The two assessed feature selection algorithms in this study have been applied on a training set of the HBR dataset in order to deduce the most selected texture features of each analyzed texture-based feature set. The evaluated feature sets in this study consist of numerous state-of-the-art texture features (Tamura, local binary patterns, gray-level run-length matrix, auto-correlation function, gray-level co-occurrence matrix, Gabor filters, Three-level Haar wavelet transform, three-level wavelet transform using 3-tap Daubechies filter and three-level wavelet transform using 4-tap Daubechies filter). In our experiments, a public corpus of historical document images provided in the context of the historical book recognition contest (HBR2013 dataset: PRImA, Salford, UK) has been used. Qualitative and numerical experiments are given in this study in order to provide a set of comprehensive guidelines on the strengths and the weaknesses of each assessed feature selection algorithm according to the used texture feature set.

Design of Time–Frequency-Localized Two-Band Orthogonal Wavelet Filter Banks

In this paper, we design time–frequency-localized two-band orthogonal wavelet filter banks using convex semidefinite programming (SDP). The sum of the time variance and frequency variance of the filter is used to formulate a real symmetric positive definite matrix for joint time–frequency localization of filters. Time–frequency-localized orthogonal low-pass filter with specified length and regularity order is designed. For nonmaximally regular two-band filter banks of length twenty, it is found that, as we increase the regularity order, the solution of the SDP converges to the filters with time–frequency product (TFP) almost same as the Daubechies maximally regular filter of length twenty. Unlike the class of Daubechies maximally regular minimum phase wavelet filter banks, a rank minimization algorithm in a SDP is employed to obtain mixed-phase low-pass filters with TFP of the filters as well as the scaling and wavelet function better than the equivalent two-band Daubechies filter bank.

Biorthogonal Halfband Perfect Reconstruction Filterbank for Multimodal Image Fusion

Objectives: To design a wavelet filter bank which helps to detect more prominently continuous changes in tumor cells. Methods/Statistical Analysis: In this paper, a method of designing two-channel wavelet base FIR filter bank using factorization of a half band filter is presented. Here factorization is done considering maximum vanishing moments for construction of decomposition as well as reconstruction filters. The 14th order maximally flat halfband filter is proposed with factorization, leading to design of 8/8 orthogonal and 9/7 & 6/10 symmetric filters. Findings: The fusion performance of designed wavelet filter bank is evaluated using various performance metrics, like, cross entropy, standard deviation, mean square error and PSNR. The results are compared with the Daubechies filter bank where db4 is used for implementation. It is clear from the results that designed filter bank improves fusion performance. Further, proposed filters have maximum number of vanishing moments which gives smooth scaling and wavelet functions and consequently provides flat frequency response. Application/Improvements: The designed 8/8 orthogonal wavelet filters are implemented in fusion application for multimodal biomedical images of a subject for detection of an abnormality (cancerous growth). The novelty of this method is the adaptive design of the filterbank for the given multimodal images, so that fused images shall have more clarity, further, it will help to improve the results with enhancement in the entropy levels of fused image. Keywords: Filter Banks, Half Band Filter, Medical Image Processing, Multimodal Image Fusion, Spectral Factorization, Wavelet Transforms

New wavelet based full-approximation scheme for the numerical solution of nonlinear elliptic partial differential equations

Recently, wavelet analysis application has dragged the attention of researchers in a wide variety of practical problems, particularly for the numerical solution of nonlinear partial differential equations. Based on Daubechies filter coefficients, a modified method using wavelet intergrid operators known as new wavelet based full-approximation scheme (NWFAS) similar to multigrid full-approximation scheme (FAS) is developed for the numerical solution of nonlinear elliptic partial differential equations. The present method gives higher accuracy in terms of better convergence with low CPU time. The results of tested examples of proposed method show better performance which is demonstrated through the illustrative examples.

Influence of normalization and color space to color texture classification

Color texture classification has recently attracted significant attention due to its multiple applications. The color texture images depend on the texture surface and its albedo, the illumination, the camera and its viewing position. A key problem to get an acceptable performance is the ambient illumination, which can vary the perceived structures in the surface. Given a color texture classification problem, it would be desirable to know which is the best approach to solve the problem making the minimal assumptions about the illumination conditions. The present work does an exhaustive evaluation of the state-of-the-art color texture classification methods, considering 5 different color spaces, 12 normalization methods to achieve illumination invariances, 19 texture feature vectors and 23 pure color feature vectors. Our experiments allow to conclude that parallel approaches are better than integrative approaches for color texture classification achieving the first positions in the Friedman ranking. Multiresolution Local Binary Patterns (MLBP) are the best intensity texture features, followed by wavelet and Gabor filters combined with luminance–chrominance color spaces (Lab and Lab2000HL), and for pure color classification the best are First Order Statistics (FOS) calculated in RGB color space. For intensity texture features, the learning methods work better on the four smallest datasets, although they could not be tested in other four bigger datasets due to its huge computational cost, nor with color texture classification. Normalization and color spaces slightly increase the average accuracy of color texture classification, although the differences achieved using normalization are not statistically significant in a paired T-Test. Lab2000HL and RGB are the best color spaces, but the former is the slowest one. Regarding elapsed time, the best vector features MLBP for intensity texture, Daub4 (Daubechies filters using mean and variance statistics) for color texture and FOS, for pure color are nearly the fastest or are in the middle interval of all the tested methods.

Nonintrusive Load Monitoring Using Wavelet Design and Machine Learning

This paper presents a new concept based on wavelet design and machine learning applied to nonintrusive load monitoring. The wavelet coefficients of length-6 filter are determined using procrustes analysis and are used to construct new wavelets to match the load signals to be detected, unlike previous work which used previously designed wavelet functions that are special cases of Daubechies filters to suit other nonpower system applications such as communications and image processing. The results of applying the new concept to a test system consisting of four loads have shown that the newly designed wavelet can improve the prediction accuracy compared with that obtained using Daubechies filter of order three while keeping the prominent features of the pattern in the detail levels.

Iris Recognition Using Wavelet Transform and Artificial Neural Networks

In this approach to get more accuracy of the iris recognition, is composed of many steps: capturing the iris image, determining the location of the iris boundaries, normalization, preprocessed using median filter to remove noise, using wavelet transform for two types of filter, Haar and Daubechies (db4), in order to extract the features and finally using the matching by artificial feed forward neural network with back propagation algorithm (FFBNN) for training and testing iris image. In this proposed system, two database systems are used. The first is CASIA database system (version 1.0) (Chinese Academy of Sciences Institute of Automation). And, the second is REAL database system by using real persons and each person takes many images for recognition through camera Mobile Type of Galaxy Note3. In CASIA System, the iris recognition rate for Haar filter was 84.2% and for Daubechies filter was 92.8%, while in Real system, the iris recognition rate for Haar filter was 90% and for Daubechies filter was 98.7%, this means the Daubechies filter was the best in time and error from the Haar filter. Finally, this system is efficient, because the performance measurement of FAR was 0%. The results and the experiments were implemented by P4 computer and the software package MATLAB (R2011a).

Traditional Psychoacoustic Model and Daubechies Wavelets for Enhanced Speech Coder Performance

Speech compression techniques based on the traditional psychoacoustic model have been proposed by many researchers. We propose the Discrete Wavelet Transform (DWT) supported by the same psychoacoustic model for speech compression. This paper presents a traditional psychoacoustic model for processing equal partitions of the total bandwidth spectrum of audio signal frequencies in order to reduce redundancy by filtering out the tones and noise maskers in the speech signal. Here, uniform filter banks are used for efficient computation, for selection of appropriate threshold levels, and for better compression of Discrete Wavelet Transform coefficients. A Daubechies wavelet filter bank is nonlinear and asymmetric. It is equivalent to a cochlear filter in the human hearing system. The similarity between the Daubechies filter bank and our hearing system was the basis for developing a novel speech coder. Better performance in terms of the compression factor (CF) and the signal-to-noise ratio (SNR) resulted, as compared to the earlier methods.

체감형 배드민턴 게임을 위한 스윙 인식과 셔틀콕 궤적 계산 방법

ABSTRACT Recently there have been many interests on tangible sport games that can recognize the motions of players. In this paper, we propose essential technologies required for tangible games, which are methods for swing motion recognition and the calculation of shuttle cock's trajectory. When a user carries out a badminton swing while holding a smartphone with his hand, the motion signal generated by smartphone-embedded acceleration sensors is transformed into a feature vector through a Daubechies filter, and then its swing type is recognized using a k-NN based method. The method for swing motion presented herein provides an advantage in a way that a player can enjoy tangible games without purchasing a commercial motion controller. Since a badminton shuttle cock has a particular flight trajectory due to the nature of its shape, it is not easy to calculate the trajectory of the shuttle cock using simple physics rules about force and velocity. In this paper, we propose a method for calculating the flight trajectory of a badminton shuttle cock in which the wind effect is considered.

A parallel 3-D discrete wavelet transform architecture using pipelined lifting scheme approach for video coding

This article presents a parallel architecture for 3-D discrete wavelet transform (3-DDWT). The proposed design is based on the 1-D pipelined lifting scheme. The architecture is fully scalable beyond the present coherent Daubechies filter bank (9, 7). This 3-DDWT architecture has advantages such as no group of pictures restriction and reduced memory referencing. It offers low power consumption, low latency and high throughput. The computing technique is based on the concept that lifting scheme minimises the storage requirement. The application specific integrated circuit implementation of the proposed architecture is done by synthesising it using 65 nm Taiwan Semiconductor Manufacturing Company standard cell library. It offers a speed of 486 MHz with a power consumption of 2.56 mW. This architecture is suitable for real-time video compression even with large frame dimensions.

Erratum to: Forecasting Urban Water Demand Via Wavelet-Denoising and Neural Network Models. Case Study: City of Syracuse, Italy

Forecasting urban water demand can be of use in the management of water utilities. For example, activities such as water-budgeting, operation and maintenance of pumps, wells, reservoirs, and mains require quantitative estimations of water resources at specified future dates. In this study, we tackle the problem of forecasting urban water demand by means of back-propagation artificial neural networks (ANNs) coupled with wavelet-denoising. In addition, non-coupled ANN and Linear Multiple Regression were used as comparison models. We considered the case of the municipality of Syracuse, Italy; for this purpose, we used a 7 year-long time series of water demand without additional predictors. Six forecasting horizons were considered, from 1 to 6 months ahead. The main objective was to implement a forecasting model that may be readily used for municipal water budgeting. An additional objective was to explore the impact of wavelet-denoising on ANN generalization. For this purpose, we measured the impact of five different wavelet filter-banks (namely, Haar and Daubechies of type db2, db3, db4, and db5) on a single neural network. Empirical results show that neural networks coupled with Haar and Daubechies’ filter-banks of type db2 and db3 outperformed all of the following: non-coupled ANN, Multiple Linear Regression and ANN models coupled with Daubechies filters of type db4 and db5. The results of this study suggest that reduced variance in the training-set (by means of denoising) may improve forecasting accuracy; on the other hand, an oversimplification of the input-matrix may deteriorate forecasting accuracy and induce network instability.

Implementation of the 2-D Wavelet Transform into FPGA for Image

This paper presents a hardware system implementation of the of discrete wavelet transform algoritm in two dimensions for FPGA, using the Daubechies filter family of order 2 (db2). The decomposition algorithm of this transform is designed and simulated with the Hardware Description Language VHDL and is implemented in a programmable logic device (FPGA) XC3S1200E reference, Spartan IIIE family, by Xilinx, take advantage the parallels properties of these gives us and speeds processing that can reach them. The architecture is evaluated using images input of different sizes. This implementation is done with the aim of developing a future images encryption hardware system using wavelet transform for security information.

Some extremal properties of Daubechies filters and other orthonormal filters

New extremal properties of Daubechies 4-tap orthonormal filters are given: they maximize a certain functional, have the largest gain in ( 0 , π / 2 ) , and allow maximum energy compaction in [ 0 , π / 2 ] . These properties do not carry over to Daubechies filters of arbitrary length. They complement what is known about Daubechies filters and highlight the specific role of the 4-tap filter. Moreover, we demonstrate that these properties cannot be fulfilled by any other orthonormal lowpass filter, regardless of its length.

IMAGE MIRRORING AND ROTATION IN THE WAVELET DOMAIN

JPEG2000, the international standard for still image compression, uses wavelet transform. The filters used by JPEG2000 for transformation are the 9/7 Daubechies filter and the 5/3 Le Gall filter. In this paper, we present a method for image mirroring and rotation in the wavelet domain, by manipulating the transformation coefficients. Our technique requires no additional complexity and the perfect reconstruction property is preserved.