arXiv subjects

Dixon Vimalajeewa

Publications and source records attributed to Dixon Vimalajeewa.

12 recordsLinked to original sources

arXiv2026

SCOPE Shrinkage: A Unified Framework for Wavelet Denoising

We introduce Symmetric CDF Oriented Probability Enhanced (SCOPE) shrinkage, a unified family of sign-preserving shrinkage rules constructed from centered cumulative distribution functions of symmetric unimodal distributions. The proposed framework generates a broad class of attenuation profiles that interpolate between strong local shrinkage near zero and asymptotically unbiased behavior in the tails. A general formulation is developed that separates scale and shape effects through two interpretable parameters, allowing effective threshold location and transition sharpness to be controlled independently. Under explicit regularity assumptions, structural properties of SCOPE shrinkage are established, including oddness, monotonicity, continuity, contractivity, and a mixture representation that connects the rules to softened thresholding operators. A Bayesian and penalized likelihood interpretation is also developed: SCOPE rules admit even penalty representations that are nondecreasing in coefficient magnitude, and suitable subclasses arise as exact maximum a posteriori estimators under proper symmetric unimodal priors. Representative examples based on logistic, uniform, and Cauchy distributions illustrate how probabilistic shape governs shrinkage behavior. Data driven parameter selection for smooth subclasses is discussed via Stein-type unbiased risk estimation. Oracle calibrated simulation studies on standard Donoho-Johnstone test functions show that SCOPE shrinkage performs competitively with several established wavelet denoising methods, while retaining a high degree of interpretability and structural flexibility. The results highlight centered distribution functions as a natural and versatile design principle for shrinkage in wavelet denoising and related estimation problems.

stat.ME↗

arXiv2026

Machine Learning Integrated in Wavelet Shrinkage (MLShrink)

Data encountered in practice are frequently contaminated by additive noise, and wavelet shrinkage remains a fundamental tool for recovering underlying signals in nonparametric estimation. Classical procedures such as hard and soft thresholding decide whether to retain a wavelet coefficient almost entirely from its magnitude. Although effective in many settings, these rules can be too rigid for coefficients whose magnitudes fall in an intermediate region where the distinction between signal and noise is uncertain. We propose MLShrink, a two-threshold wavelet denoising procedure that combines wavelet shrinkage with machine learning. Coefficients below a lower threshold are discarded, coefficients above an upper threshold are retained, and coefficients in the intermediate band are classified using local wavelet-domain features. In this way, MLShrink preserves the simplicity of classical thresholding away from the decision boundary while allowing data-adaptive decisions for ambiguous coefficients. The paper also develops a theoretical framework tailored to this architecture. We show that MLShrink is a nonexpansive support-selection rule, derive an oracle-based risk decomposition showing that excess denoising risk is determined by classification errors on the undecided band, and establish an oracle-consistency result under suitable assumptions on classifier performance. Simulation experiments on standard benchmark signals indicate that MLShrink is competitive with several established wavelet shrinkage methods and is especially effective for signals with irregular, edge-rich, or non-smooth structure. These findings suggest that learned decisions on the intermediate threshold band provide a useful and interpretable connection between classical wavelet denoising and modern statistical learning.

stat.ME↗

arXiv2025

A Multiscale Approach for Enhancing Weak Signal Detection

Stochastic resonance (SR), a phenomenon originally introduced in climate modeling, enhances signal detection by leveraging optimal noise levels within non-linear systems. Traditional SR techniques, mainly based on single-threshold detectors, are limited to signals whose behavior does not depend on time. Often large amounts of noise are needed to detect weak signals, which can distort complex signal characteristics. To address these limitations, this study explores multi-threshold systems and the application of SR in multiscale applications using wavelet transforms. In the multiscale domain signals can be analyzed at different levels of resolution to better understand the underlying dynamics. We propose a double-threshold detection system that integrates two single-threshold detectors to enhance weak signal detection. We evaluate it both in the original data domain and in the multiscale domain using simulated and real-world signals and compare its performance with existing methods. Experimental results demonstrate that, in the original data domain, the proposed double-threshold detector significantly improves weak signal detection compared to conventional single-threshold approaches. Its performance is further improved in the frequency domain, requiring lower noise levels while outperforming existing detection systems. This study advances SR-based detection methodologies by introducing a robust approach to weak signal identification, with potential applications in various disciplines.

eess.SP↗

arXiv2025

A Noise Resilient Approach for Robust Hurst Exponent Estimation

Understanding signal behavior across scales is vital in areas such as natural phenomena analysis and financial modeling. A key property is self-similarity, quantified by the Hurst exponent (H), which reveals long-term dependencies. Wavelet-based methods are effective for estimating H due to their multi-scale analysis capability, but additive noise in real-world measurements often degrades accuracy. We propose Noise-Controlled ALPHEE (NC-ALPHEE), an enhancement of the Average Level-Pairwise Hurst Exponent Estimator (ALPHEE), incorporating noise mitigation and generating multiple level-pairwise estimates from signal energy pairs. A neural network (NN) combines these estimates, replacing traditional averaging. This adaptive learning maintains ALPHEE's behavior in noise-free cases while improving performance in noisy conditions. Extensive simulations show that in noise-free data, NC-ALPHEE matches ALPHEE's accuracy using both averaging and NN-based methods. Under noise, however, traditional averaging deteriorates and requires impractical level restrictions, while NC-ALPHEE consistently outperforms existing techniques without such constraints. NC-ALPHEE offers a robust, adaptive approach for H estimation, significantly enhancing the reliability of wavelet-based methods in noisy environments.

stat.ML↗

arXiv2024

Ovarian Cancer Diagnostics using Wavelet Packet Scaling Descriptors

Detecting early-stage ovarian cancer accurately and efficiently is crucial for timely treatment. Various methods for early diagnosis have been explored, including a focus on features derived from protein mass spectra, but these tend to overlook the complex interplay across protein expression levels. We propose an innovative method to automate the search for diagnostic features in these spectra by analyzing their inherent scaling characteristics. We compare two techniques for estimating the self-similarity in a signal using the scaling behavior of its wavelet packet decomposition. The methods are applied to the mass spectra using a rolling window approach, yielding a collection of self-similarity indexes that capture protein interactions, potentially indicative of ovarian cancer. Then, the most discriminatory scaling descriptors from this collection are selected for use in classification algorithms. To assess their effectiveness for early diagnosis of ovarian cancer, the techniques are applied to two datasets from the American National Cancer Institute. Comparative evaluation against an existing wavelet-based method shows that one wavelet packet-based technique led to improved diagnostic performance for one of the analyzed datasets (95.67% vs. 96.78% test accuracy, respectively). This highlights the potential of wavelet packet-based methods to capture novel diagnostic information related to ovarian cancer. This innovative approach offers promise for better early detection and improved patient outcomes in ovarian cancer.

stat.AP↗

arXiv2023

Utilizing Wavelet Transform in the Analysis of Scaling Dynamics for Milk Quality Evaluation

Food safety and quality are paramount concerns worldwide, especially concerning nutritional quality and its impact on human health. Ensuring the accuracy and efficiency of milk quality assessment is vital for maintaining the quality of dairy farm produce. Milk spectral data, Mid-infrared spectra (MIRS) of milk samples, are frequently employed for milk quality evaluations, encompassing various milk quality parameters. However, conventional milk quality analyses have overlooked the scaling nature, known as stochastic similarity in different scales, inherent in milk spectral data. Wavelet transforms are among the tools used in these analyses, although they are primarily used as data pre-processing techniques without fully realizing their potential in extracting valuable insights. The primary purpose of this study is to demonstrate the importance of accounting for scaling properties in assessing milk quality. A set of 12 descriptors is computed to characterize scaling properties in milk spectral data within the wavelet domain. These descriptors are then assessed for their effectiveness in milk quality assessments utilizing 18 different milk quality parameters. They notably demonstrated comparable performance to existing methods while utilizing fewer features when applied to an MIRS dataset. This innovative approach holds substantial promise for advancing the field of milk quality assessment, offering a means to achieve more accurate and efficient evaluations while shedding light on previously unexplored aspects of milk spectral data.

stat.AP↗

arXiv2023

A Method for Detecting Murmurous Heart Sounds based on Self-similar Properties

A heart murmur is an atypical sound produced by the flow of blood through the heart. It can be a sign of a serious heart condition, so detecting heart murmurs is critical for identifying and managing cardiovascular diseases. However, current methods for identifying murmurous heart sounds do not fully utilize the valuable insights that can be gained by exploring intrinsic properties of heart sound signals. To address this issue, this study proposes a new discriminatory set of multiscale features based on the self-similarity and complexity properties of heart sounds, as derived in the wavelet domain. Self-similarity is characterized by assessing fractal behaviors, while complexity is explored by calculating wavelet entropy. We evaluated the diagnostic performance of these proposed features for detecting murmurs using a set of standard classifiers. When applied to a publicly available heart sound dataset, our proposed wavelet-based multiscale features achieved comparable performance to existing methods with fewer features. This suggests that self-similarity and complexity properties in heart sounds could be potential biomarkers for improving the accuracy of murmur detection.

eess.SP↗

arXiv2022

Early Detection of Ovarian Cancer by Wavelet Analysis of Protein Mass Spectra

Accurate and efficient detection of ovarian cancer at early stages is critical to ensure proper treatments for patients. Among the first-line modalities investigated in studies of early diagnosis are features distilled from protein mass spectra. This method, however, considers only a specific subset of spectral responses and ignores the interplay among protein expression levels, which can also contain diagnostic information. We propose a new modality that automatically searches protein mass spectra for discriminatory features by considering the self-similar nature of the spectra. Self-similarity is assessed by taking a wavelet decomposition of protein mass spectra and estimating the rate of level-wise decay in the energies of the resulting wavelet coefficients. Level-wise energies are estimated in a robust manner using distance variance, and rates are estimated locally via a rolling window approach. This results in a collection of rates that can be used to characterize the interplay among proteins, which can be indicative of cancer presence. Discriminatory descriptors are then selected from these evolutionary rates and used as classifying features. The proposed wavelet-based features are used in conjunction with features proposed in the existing literature for early stage diagnosis of ovarian cancer using two datasets published by the American National Cancer Institute. Including the wavelet-based features from the new modality results in improvements in diagnostic performance for early-stage ovarian cancer detection. This demonstrates the ability of the proposed modality to characterize new ovarian cancer diagnostic information.

cs.LG↗

arXiv2022

Gamma-Minimax Wavelet Shrinkage with Three-Point Priors

In this paper we propose a method for wavelet denoising of signals contaminated with Gaussian noise when prior information about the $L^2$-energy of the signal is available. Assuming the independence model, according to which the wavelet coefficients are treated individually, we propose a simple, level dependent shrinkage rules that turn out to be $Γ$-minimax for a suitable class of priors. The proposed methodology is particularly well suited in denoising tasks when the signal-to-noise ratio is low, which is illustrated by simulations on the battery of standard test functions. Comparison to some standardly used wavelet shrinkage methods is provided.

stat.ME↗

arXiv2021

Channel Capacity of Starch and Glucose Molecular Communications in the Small Intestine Digestive Tract

The emerging field of Molecular Communication (MC) aims to characterize biological-based signaling environment through information that are encoded into molecules. Since the birth of this field, a number of different applications and biological systems have been characterized using MC theory. This study proposes a new application and direction for MC, focusing on the digestive system, where we characterize and model the starch and glucose propagation along the small intestine. Based on the advection-diffusion and reaction mechanisms, we define a channel capacity for the small intestine digestive tract that is dependent on the starch to glucose conversion, velocity flow within the tract, viscosity of the digest product, and length of the tract and position of the receivers for glucose absorption. The numerical results from the derived channel capacity model shows that the SI digestive capacity depends both on physiological factors of the digestive system and type of consumed food, where the digestive capacity is greater for shorter gastric emptying time, low viscosity of the digest product and efficient enzyme activity. We believe that our digital MC model of the digestive tract and lead to personalized diet for each individual, which can potentially avoid a number of different diseases (e.g., celiac disease).

q-bio.MN↗

arXiv2021

Digestive System Dynamics in Molecular Communication Perspectives

Consumption of food in excess of the required optimal nutritional requirements has already resulted in a global crisis and this is from the perspective of human health, such as obesity, as well as food waste and sustainability. In order to minimize the impact of these issues, there is a need to develop novel innovative and effective solutions that can optimally match the food consumption to the demand. This requires accurate understanding of the food digestion dynamics and its impact on each individual's physiological characteristics. This study proposes a model to characterize digestive system dynamics by using concepts from the field of Molecular Communications (MC), and this includes integrating advection-diffusion and reaction mechanisms and its role in characterizing the digestion process as a communication system. The model is then used to explore starch digestion dynamics by using communication system metrics such as delay and path loss. Our simulations found that the long gastric emptying time increases the delay in starch digestion and in turn the glucose production and absorption into the blood stream. At the same time, the enzyme activity on the hydrolyzed starch directly impacts the path loss, as higher reaction rates and lower half saturation concentration of starch results in lower path loss. Our work can lead to provide insights formulated for each individuals by creating a digital twin digestion model

cs.CE↗

arXiv2020

Block Chain and Internet of Nano-Things for Optimizing Chemical Sensing in Smart Farming

The use of Internet of Things (IoT) with the Internet of Nano Things (IoNT) can further expand decision making systems (DMS) to improve reliability as it provides a new spectrum of more granular level data to make decisions. However, growing concerns such as data security, transparency and processing capability challenge their use in real-world applications. DMS integrated with Block Chain (BC) technology can contribute immensely to overcome such challenges. The use of IoNT and IoT along with BC for making DMS has not yet been investigated. This study proposes a BC-powered IoNT (BC-IoNT) system for sensing chemicals level in the context of farm management. This is a critical application for smart farming, which aims to improve sustainable farm practices through controlled delivery of chemicals. BC-IoNT system includes a novel machine learning model formed by using the Langmuir molecular binding model and the Bayesian theory, and is used as a smart contract for sensing the level of the chemicals. A credit model is used to quantify the traceability and credibility of farms to determine if they are compliant with the chemical standards. The accuracy of detecting the chemicals of the distributed BC-IoNT approach was >90% and the centralized approach was <80%. Also, the efficiency of sensing the level of chemicals depends on the sampling frequency and variability in chemical level among farms.

eess.SP↗