Wavelet Moments Research Articles

Wavelet-based statistics for enhanced 21cm EoR parameter constraints

We propose a new approach to improve the precision of astrophysical parameter constraints for the 21cm signal from the epoch of reionisation (EoR). Our method introduces new sets of summary statistics, hereafter ‘evolution compressed’ statistics, which quantify the spectral evolution of the 2D spatial statistics computed at fixed redshift. We defined such compressed statistics for power spectrum (PS), wavelet scattering transforms (WST), and wavelet moments (WM), which also characterise non-Gaussian features. To compare these different statistics, along with the 3D power spectrum, we estimated their Fisher information on three cosmological parameters from an ensemble of simulations of 21cm EoR data, both in noiseless and noisy scenarios using Square Kilometre Array (SKA) noise levels equivalent to 100 and 1000 h of observations. We also compare wavelet statistics, in particular WST, built from standard directional Morlet wavelets, as well as from a set of isotropic wavelets derived from the binning window function of the 2D power spectrum. For the noiseless case, the compressed wavelet statistics give constraints that are up to five times more precise than those obtained from the 3D isotropic power spectrum. At the same time, for 100 h SKA noise, from which it is difficult to extract non-Gaussian features, compressed wavelet statistics still give over 30% tighter constraints. We find that the wavelet statistics with wavelets derived from the power-spectrum binning window function provide the tightest constraints of all the statistics, with the WSTs seemingly performing better than the WMs, in particular when working with noisy data. The findings of this study demonstrate that evolution-compressed statistics extract more information than usual 3D isotropic power-spectra approaches and that our wavelet-based statistics can consistently outmatch power-spectrum-based statistics. When constructing such wavelet-based statistics, we also emphasise the need to choose a set of wavelets with an appropriate spectral resolution concerning the astrophysical process studied.

Application of Hybrid ANN Techniques for Drought Forecasting in the Semi-Arid Region of India.

The intensity and frequency of diverse hydro-meteorological disasters viz., extreme droughts, severe floods, and cyclones have increasing trends due to unsustainable management of land and water resources, coupled with increasing industrialization, urbanization and climate change. This study focuses on the forecasting of drought using selected Artificial Neural Network (ANN)-based models to enable decision-makers to improve regional water management plans and disaster mitigation/reduction plans. Four ANN models were developed in this study, viz., one conventional ANN model and three hybrid ANN models: (a) Wavelet based-ANN (WANN), (b) Bootstrap based-ANN (BANN), and (c) Wavelet-Bootstrap based-ANN (WBANN). The Standardized Precipitation Evapotranspiration Index (SPEI), the best drought index identified for the study area, was used as a variable for drought forecasting. Three drought indices, such as SPEI-3, SPEI-6 and SPEI-12 respectively representing "short-term", "intermediate-term", and "long-term" drought conditions, were forecasted for 1-month to 3-month lead times for six weather stations over the study area. Both statistical and graphical indicators were considered to assess the performance of the developed models. For the hybrid wavelet model, the performance was evaluated for different vanishing moments of Daubechies wavelets and decomposition levels. The best-performing bootstrap-based model was further used for analysing the uncertainty associated with different drought forecasts. Among the models developed for drought forecasting for 1 to 3 months, the performances of the WANN and WBANN models are superior to the simple ANN and BANN models for the SPEI-3, SPEI-6, and SPEI-12 up to the 3-month lead time. The performance of the WANN and WBANN models is the best for SPEI-12 (MAE = 0.091-0.347, NSE = 0.873-0.982) followed by SPEI-6 (MAE = 0.258-0.593; NSE = 0.487-0.848) and SPEI-3 (MAE = 0.332-0.787, NSE = 0.196-0.825) for all the stations up to 3-month lead time. This finding is supported by the WBANN analyze uncertainties as narrower band width for SPEI-12 (0.240-0.898) as compared to SPEI-6 (0.402-1.62) and SPEI-3 (0.474-2.304). Therefore, the WBANN model is recommended for the early warning of drought events as it facilitates the uncertainty analysis of drought forecasting results.

The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series

The global navigation satellite system (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow to study global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work, we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time-series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogenous variables: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used maximum likelihood estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results (theoretical and obtained in simulations) show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach have important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations (some of them being recorded over several decades) quickly becomes computationally prohibitive. Compared to standard likelihood-based methods, the GMWMX has a considerably reduced algorithmic complexity of order mathcal {O}{log (n) n} for a time series of length n. Thus, the GMWMX appears to provide a reduction in processing time of a factor of 10–1000 compared to likelihood-based methods depending on the considered stochastic model, the length of the time series and the amount of missing data. As a consequence, the proposed method allows the estimation of large-scale problems within minutes on a standard computer. We validate the performances of our method via Monte Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power law or Matérn processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.

An Algorithm for Online Stochastic Error Modeling of Inertial Sensors in Urban Cities.

Regardless of whether the global navigation satellite system (GNSS)/inertial navigation system (INS) is integrated or the INS operates independently during GNSS outages, the stochastic error of the inertial sensor has an important impact on the navigation performance. The structure of stochastic error in low-cost inertial sensors is quite complex; therefore, it is difficult to identify and separate errors in the spectral domain using classical stochastic error methods such as the Allan variance (AV) method and power spectral density (PSD) analysis. However, a recently proposed estimation, based on generalized wavelet moment estimation (GMWM), is applied to the stochastic error modeling of inertial sensors, giving significant advantages. Focusing on the online implementation of GMWM and its integration within a general navigation filter, this paper proposes an algorithm for online stochastic error calibration of inertial sensors in urban cities. We further develop the autonomous stochastic error model by constructing a complete stochastic error model and determining model ranking criterion. Then, a detecting module is designed to work together with the autonomous stochastic error model as feedback for the INS/GNSS integration. Finally, two experiments are conducted to compare the positioning performance of this algorithm with other classical methods. The results validate the capability of this algorithm to improve navigation accuracy and achieve the online realization of complex stochastic models.

On Performance Evaluation of Inertial Navigation Systems: The Case of Stochastic Calibration

In this work we address the problem of rigorously evaluating the performances of an inertial navigation system during its design phase in presence of multiple alternative choices. We introduce a framework based on Monte-Carlo simulations in which a standard extended Kalman filter is coupled with realistic and user-configurable noise generation mechanisms to recover a reference trajectory from noisy measurements. The evaluation of several statistical metrics of the solution, aggregated over hundreds of simulated realizations, provides reasonable estimates of the expected performances of the system in real-world conditions. This framework allows the user to make a choice between alternative setups. To show the generality of our approach, we consider an example application to the problem of stochastic calibration. Two competing stochastic modeling techniques, namely, the widely popular Allan variance linear regression, and the emerging generalised method of wavelet moments, are rigorously compared in terms of the framework’s defined metrics and in multiple scenarios. We find that the latter provides substantial advantages for certain classes of inertial sensors. Our framework allows to consider a wide range of problems related to the quantification of navigation system performances, such as the robustness of integrated navigation systems (such as INS/GNSS) with respect to outliers or other modeling imperfections. While real world experiments are essential to assess to performance of new methods, they tend to be costly and are typically unable to lead to a sufficient number of replicates to provide suitable estimates of, for example, the correctness of the estimated uncertainty. Therefore, our method can contribute in bridging the gap between these experiments and pure statistical consideration as usually found in the stochastic calibration literature.

On the integrated mean squared error of wavelet density estimation for linear processes

Let $\{X_n: n\in \N\}$ be a linear process with density function $f(x)\in L^2(\R)$. We study wavelet density estimation of $f(x)$. Under some regular conditions on the characteristic function of innovations, we achieve, based on the number of nonzero coefficients in the linear process, the minimax optimal convergence rate of the integrated mean squared error of density estimation. Considered wavelets have compact support and are twice continuously differentiable. The number of vanishing moments of mother wavelet is proportional to the number of nonzero coefficients in the linear process and to the rate of decay of characteristic function of innovations. Theoretical results are illustrated by simulation studies with innovations following Gaussian, Cauchy and chi-squared distributions.

Development of a new machine vision algorithm to estimate potato's shape and size based on support vector machine

AbstractDevelopment of a new machine vision‐based algorithm, to estimate potato's shape and size, will have great significance to agricultural industry in developing countries. Machine vision, one of hot technique, uses machines to execute measurement, calculating, and judgment instead of human eyes. In this study, a new machine vision algorithm, based on support vector machine, was proposed for estimating potato's shape and size. After captured the square RGB image with 512 × 512 pixels, the original image was processed by gray scale and linear transformation, filtering, entity, and boundary detecting. Then, geometric characteristics, image wavelet moment, and fractal dimension of boundary were extracted for marking the potato's characteristic. In addition, the effect of four kind of support vector machine (SVM) kernel function was comparing by several experiments with 64 potato samples. By experimental confirmation, SVM based on the polynomial kernel is more suitable for discriminating potato's shape with an accuracy of 88.89%; SVM based on the linear kernel is more suitable for estimating potato's size with an accuracy of 87.41%.Practical applicationsPotato is a high‐yield, nutrient‐rich crop with high nutritional value. This study proposes a potato shape and size estimation algorithm based on machine vision. Through experimental verification, the detection accuracy of the algorithm initially meets the actual engineering application. The shape and size of potatoes can be detected to classify potatoes. In the process of food processing such as potato chips, the classification of potatoes is conducive to improving the quality of food processing.

IR-MF-SVMe: Image Retrieval using Multiple Features Extraction with Support Vector Machine ensemble

Image representation is a widespread strategy of image retrieval based on appearance, shape information. The traditional feature representation methods ignore hidden information that exists in the dataset samples; it reduces the discriminative performance of the classifier and excludes various geometric and photometric variations consideration in obtaining the features; these degrade retrieval performance. Hence, proposed multiple features fusion and Support Vector Machines Ensemble (IR-MF-SVMe); an Image Retrieval framework to enhance the performance of the retrieval process. The Color Histogram (CH), Color Auto-Correlogram (CAC), Color Moments (CM), Gabor Wavelet (GW), and Wavelet Moments (WM) descriptors are used to extract multiple features that separate the element vectors of images in representation. The multi-class classifier is constructed with the aggregation of binary Support Vector Machines, which decrease the count of false positives within the interrelated semantic classes. The proposed framework is validated on the WANG dataset and results in the accuracy of 84% for the individual features and 86% for the fused features related to the state-of-the-arts.

Fast Job Recognition and Sorting Based on Image Processing

With the advancement of artificial intelligence (AI) and the upgrading of intelligent manufacturers, the development of intelligent manufacturing is now propelled by the replacement of inefficient traditional assembly machines and operators with machine vision (MV)-based industrial robots. The classic job recognition and positioning algorithm has multiple shortcomings, such as high complexity, manual design of similarity function, and susceptibility to noise disturbance. To solve these shortcomings, this study presents a fast job recognition and sorting method based on image processing. Firstly, the extraction approach for wavelet moment features and wavelet descriptors was introduced, and the feature fusion based on echo state network (ESN) was detailed. Then, the authors explained the idea of job template matching, and described how to measure similarity and terminate the measurement during template matching. Experimental results fully manifest the effectiveness of our strategy for fast job recognition and sorting. Our method offers a new solution to rapid recognition and sorting of objects in other fields.

Robust Two-Step Wavelet-Based Inference for Time Series Models

Latent time series models such as (the independent sum of) ARMA(p, q) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv) solutions that address (i), (ii), and (iii) simultaneously do not exist in practice. This paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. We first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator, we then develop the asymptotic properties of two-step robust estimators using the framework of the generalized method of wavelet moments (GMWM). Simulation studies illustrate the good finite sample performance of the robust GMWM estimator and applied examples highlight the practical relevance of the proposed approach.

Robust Magnification Independent Colon Biopsy Grading System over Multiple Data Sources

Automated grading of colon biopsy images across all magnifications is challenging because of tailored segmentation and dependent features on each magnification. This work presents a novel approach of robust magnification-independent colon cancer grading framework to distinguish colon biopsy images into four classes: normal, well, moderate, and poor. The contribution of this research is to develop a magnification invariant hybrid feature set comprising cartoon feature, Gabor wavelet, wavelet moments, HSV histogram, color auto-correlogram, color moments, and morphological features that can be used to characterize different grades. Besides, the classifier is modeled as a multiclass structure with six binary class Bayesian optimized random forest (BO-RF) classifiers. This study uses four datasets (two collected from Indian hospitals—Ishita Pathology Center (IPC) of 4X, 10X, and 40X and Aster Medcity (AMC) of 10X, 20X, and 40X—two benchmark datasets—gland segmentation (GlaS) of 20X and IMEDIATREAT of 10X) comprising multiple microscope magnifications. Experimental results demonstrate that the proposed method outperforms the other methods used for colon cancer grading in terms of accuracy (97.25%-IPC, 94.40%-AMC, 97.58%-GlaS, 99.16%-Imediatreat), sensitivity (0.9725-IPC, 0.9440-AMC, 0.9807-GlaS, 0.9923-Imediatreat), specificity (0.9908-IPC, 0.9813-AMC, 0.9907-GlaS, 0.9971-Imediatreat) and F-score (0.9725-IPC, 0.9441-AMC, 0.9780-GlaS, 0.9923-Imediatreat). The generalizability of the model to any magnified input image is validated by training in one dataset and testing in another dataset, highlighting strong concordance in multiclass classification and evidencing its effective use in the first level of automatic biopsy grading and second opinion.

Image Classification Schemes Based on Statistical Moments of Wavelet and Sliced Radial Energy Distribution of DCT

Texture recognition is used in various pattern recognition applications and texture classification that possess a characteristic appearance. This research paper aims to provide an improved scheme to provide enhanced classification decisions and to decrease processing time significantly. This research studied the discriminating characteristics of textures by extracting them from various texture images using discrete Wavelate transform (DWT) and discrete Cosine transform DCT. Two sets of features are proposed; the first set was extracted using the traditional DCT, while the second used DWT. The features from the Cosine domain are calculated using the radial distribution of spectra, while for those extracted from Wavelet was statistical distribution of various relative moments. Four types of Euclidean distance metrics were used for classification decision purposes. The considered method was applied on 475 classes of textures belonged to 32 sets from Salzburg Texture Image Database, each set holding 16 images per class, so the a total of 7600 images were tested. Each image was separated into three bands of color component (i.e., red, green, blue). Concepts of average and standard deviation were calculated to determine the inter/intra scatter analysis for each feature to find out the best discriminating features that can be used. The final result of DWT was 99.98 for the testing sets and 99.71 for the training sets, while the final result of DCT was 99.06 for the testing sets and 96.77 for the training sets.

A simple and quick method to detect adulterated sesame oil using 3D fluorescence spectra.

Adulterated sesame oil seriously damages the interests of consumers and the health of market. In this paper, a simple, fast and real-time model for identifying adulterated sesame oil (ASO) was proposed by combining 3D fluorescence spectra with wavelet moments (WMs). First, noise and data volume of the experimental data were reduced by wavelet multiresolution decomposition (WMRSD), which improved the stability and real-time of the model. Next, WMs were used to extract the features of the 3D fluorescence spectra and proved to be effective by hierarchical clustering results. Then, the qualitative quality of WMs of the same orders, different orders and the combinations were evaluated by Dunn's validity index (DVI), and the rules were given, respectively. Finally, the target WMs for identifying ASO were determined. This model is simple and fast, and expandable to online measurement, providing a reference for identification and adulteration of vegetable oils.

A principal component analysis-based feature dimensionality reduction scheme for content-based image retrieval system

In Content-Based Image Retrieval (CBIR) system, one approach of image representation is to employ combination of low-level visual features cascaded together into a flat vector. While this presents more descriptive information, it however poses serious challenges in terms of high dimensionality and high computational cost of feature extraction algorithms to deployment of CBIR on platforms (devices) with limited computational and storage resources. Hence, in this work a feature dimensionality reduction technique based on Principal Component Analysis (PCA) is implemented. Each image in a database is indexed using 174 dimensional feature vector comprising of 54-dimensional Colour Moments (CM54), 32-bin HSV-histogram (HIST32), 48-dimensional Gabor Wavelet (GW48) and 40-dimensional Wavelet Moments (MW40). The PCA scheme was incorporated into a CBIR system that utilized the entire feature vector space. The k-largest Eigenvalues that yielded a not more than 5% degradation in mean precision were retained for dimensionality reduction. Three image databases (DB10, DB20 and DB100) were used for testing. The result obtained showed that with 80% reduction in feature dimensions, tolerable loss of 3.45, 4.39 and 7.40% in mean precision value were achieved on DB10, DB20 and DB100.

SAR target classification using multi-aspect multi-feature collaborative representation

ABSTRACT In this paper, a novel approach is proposed for Synthetic Aperture Radar (SAR) target classification based on multi-aspect multi-feature collaborative representation. Firstly, principal component analysis (PCA), wavelet and 2-dimensional slice Zernike moments (2DSZM) features are extracted from SAR images. Next, based on the strong correlation among the adjacent aspect SAR target images, we extend the basic collaborative representation classification (CRC) model to a neighbourhood multi-aspect CRC model. For each feature of the current test sample, neighbourhood multi-aspect test samples are regarded as the input to the model, then the temporary label is obtained for the current test sample under this feature. Finally, the temporary label is fused using the voting method to get the final classification result. The novelty of the proposed method is to improve the performance of target classification by integrating representation learning ability of different features and exploiting neighbourhood multi-aspect correlation. Experiments are investigated on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset. The results show that the proposed algorithm can achieve a 98.52% overall accuracy and is superior to state-of-the-art methods for SAR target classification.

Feature extraction and measurement algorithm based on color in image database

Image recognitionan is an important part of pattern recognition, It has been widely used in modern production and life. Using computer technology and modern information processing technology to complete human visual cognition and understanding. Thus, It have become a hot topic about how to study im age recognition based on medical color feature extraction. This study firstly studied the existing literature, explored and analyzed relevant theories and technologies, and studied several algorithms related to current image recognition. Then the image recognition algorithm based on wavelet moment and support vector machine is combined with the artificial intelligence technology based on image feature extraction theory to establish the color medical image recognition algorithm based on wavelet moment and support vector machine. In order to verify the feasibility and advancedness of the new algorithm, practical experiments are carried out, and the experimental results are compared and analyzed by statistical method. The concrete chart proves the correctness of the conclusion. The final of the new algorithm is proved to be successful.

Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration

The task of inertial sensor calibration has required the development of various techniques to take into account the sources of measurement error coming from such devices. The calibration of the stochastic errors of these sensors has been the focus of increasing amount of research in which the method of reference has been the so-called "Allan variance slope method" which, in addition to not having appropriate statistical properties, requires a subjective input which makes it prone to mistakes. To overcome this, recent research has started proposing "automatic" approaches where the parameters of the probabilistic models underlying the error signals are estimated by matching functions of the Allan variance or Wavelet Variance with their model-implied counterparts. However, given the increased use of such techniques, there has been no study or clear direction for practitioners on which approach is optimal for the purpose of sensor calibration. This paper formally defines the class of estimators based on this technique and puts forward theoretical and applied results that, comparing with estimators in this class, suggest the use of the Generalized Method of Wavelet Moments as an optimal choice.

Multivariate Signal Modeling With Applications to Inertial Sensor Calibration

The common approach to inertial sensor calibration for navigation purposes has been to model the stochastic error signals of individual sensors independently, whether as components of a single inertial measurement unit (IMU) in different directions or arrayed in the same direction for redundancy. These signals usually have an extremely complex spectral structure that is often described using latent (or composite) models composed by a sum of underlying models. A large amount of research in this domain has been focused on the latter aspect through the proposal of various methods that have been able to improve the estimation of these models both from a computational and a statistical point of view. However, the separate calibration of the individual sensors is still unable to take into account the dependence between each of them which can have an important impact on the precision of the navigation systems. In this paper, we develop a new approach to simultaneously model both the individual signals and the dependence between them by studying the quantity called Wavelet Cross-Covariance and using it to extend the application of the Generalized Method of Wavelet Moments. This new method can be used in other settings for time series modeling, especially in cases where the dependence among signals may be hard to detect. Moreover, in the field of inertial sensor calibration, this approach can deliver important contributions among which the possibility to test dependence between sensors, integrate their dependence within the navigation filter and construct an optimal virtual sensor that can be used to simplify and improve navigation accuracy. The advantages of this method and its usefulness for inertial sensor calibration are highlighted through a simulation study and an applied example with a small array of XSens MTi-G IMUs.

Notice of Retraction Effects vanishing moments of discrete wavelet transform on MRI image compression algorithms

Notice of Retraction-----------------------------------------------------------------------After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of APTIKOM's Publication Principles.We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.The presenting author of this paper has the option to appeal this decision by contacting ij.aptikom@gmail.com.-----------------------------------------------------------------------Image data usually contain considerable quantity of data that is redundant and much irrelevant, whereas an image compression technique overcomes this by compressing the amount of data required to represent the image. In this work, Discrete Wavelet Transform based image compression algorithm is implemented for decomposing the image. The various encoding schemes such as Embedded Zero wavelet, (EZW), Set Partitioning In Hierarchical Trees(SPIHT) and Spatial orientation Tree Wavelet(STW) are used and their performances in the compression is evaluated and also the effectiveness of different wavelets with various vanishing moments are analyzed based on the values of PSNR, Compression ratio, Means square error and bits per pixel. The optimum compression algorithm is also found based on the results.

Selection of Vanishing moments of Symlet and Coiflet Wavelets on CT Images

The main aim of the work is to develop image compression algorithms with high quality and compression ratio. The objective also includes finding out an best algorithm for medical image compression techniques. The objective is also alert towards the choice of the developed image compression algorithm, which do not modify the characterization behavior of the image. In this paper, image compression algorithm based on discrete symlet and coiflet wavelet transform is implemented for decomposing the image. The selection of different vanishing moments are discussed based on the values of peak signal to noise ratio (PSNR), compression ratio (CR), means square error (MSE) and bits per pixel (BPP). The optimum moments for compression are also chosen based on the results.