Related papers: Bayesian estimation of the multifractality paramet…

In this work, we investigate the estimation of a parameter $f$ in PDEs using Bayesian procedures, and focus on posterior distributions constructed using Gaussian process priors, and its variational approximation. We establish contraction…

Multifractal analysis has revealed regularities in many self-seeding phenomena, yet its use in modern deep learning remains limited. Existing end-to-end multifractal methods rely on heavy pooling or strong feature-space decimation, which…

The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…

We present a novel method for determining multi-fractal properties from experimental data. It is based on maximising the likelihood that the given finite data set comes from a particular set of parameters in a multi-parameter family of well…

Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…

In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the…

Spatial and spectral approaches are two major approaches for image processing tasks such as image classification and object recognition. Among many such algorithms, convolutional neural networks (CNNs) have recently achieved significant…

Advanced geometrical nanometrology is critical for process control in semiconductor manufacturing, supporting applications in, e.g., photonic integrated circuits, nanoelectronics, and emerging quantum and optoelectronic technologies.…

Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…

Image segmentation is a fundamental step for the interpretation of Remote Sensing Images. Clustering or segmentation methods usually precede the classification task and are used as support tools for manual labeling. The most common…

We present a novel method to estimate the multifractal spectrum of point distributions. The method incorporates two motivated criteria (barycentric pivot point selection and non-overlapping coverage) in order to reduce edge effects, improve…

In this paper, we present a novel Bayesian approach for estimating spectral and range profiles from single-photon Lidar waveforms associated with single surfaces in the photon-limited regime. In contrast to classical multispectral Lidar…

Complex systems are composed of mutually interacting components and the output values of these components are usually long-range cross-correlated. We propose a method to characterize the joint multifractal nature of such long-range cross…

Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation…

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…

A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed…

Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…

Ongoing advances in microbiome profiling have allowed unprecedented insights into the molecular activities of microbial communities. This has fueled a strong scientific interest in understanding the critical role the microbiome plays in…