Related papers: Using Wavelet Decomposition to Determine the Dimen…
Large-scale structure (LSS) analysis in galaxy surveys is a powerful cosmological probe but is limited by tracer bias, which can obscure underlying information and weaken parameter constraints. Existing methods either model bias or restrict…
Context. Images of spatially resolved astrophysical objects contain a wealth of morphological and dynamical information, and effective extraction of this information is of paramount importance for understanding the physics and evolution of…
Velocity measurements made from multiple-epoch astronomical images of evolving objects with optically thin continuum emission (e.g. as relativistic jets or expanding supernova shells) may be confused as a result of the overlap of…
We consider wavelets as a tool to perform a variety of tasks in the context of analyzing cosmic microwave background (CMB) maps. Using Spherical Haar Wavelets we define a position and angular-scale-dependent measure of power that can be…
The James Webb Space Telescope (JWST) is expected to revolutionize our understanding of Jovian worlds over the coming decade. However, as we push towards characterizing cooler, smaller, "terrestrial-like" planets, dedicated next-generation…
Wavelet analysis is proposed as a new tool for studying the large-scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of one-dimensional cosmological density fluctuations is performed. In contrast…
Atomization stretches and folds the liquid-gas interface before fragmenting it into ligaments and droplets, making fractal measures a natural descriptor of the breakup state. We examine this idea in two-dimensional volume-of-fluid direct…
A method for measuring the spectrum of a density field by a discrete wavelet space-scale decomposition (SSD) has been studied. We show how the power spectrum can effectively be described by the father function coefficients (FFC) of the…
Wavelet decomposition is a method that has been applied to signal processing in a wide range of subjects. The decomposition isolates small scale features of a signal from large scale features, while also maintaining information about where…
Large scale density modes are difficult to measure because they are sensitive to systematic observational errors in galaxy surveys, but we can study them indirectly by observing their impact on small scale perturbations. Cosmological…
Extracting non-Gaussian information from the non-linear regime of structure formation is key to fully exploiting the rich data from upcoming cosmological surveys probing the large-scale structure of the universe. However, due to theoretical…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
We propose a new, efficient multi-scale method to decompose a map (or signal in general) into components maps that contain structures of different sizes. In the widely-used wave transform, artifacts containing negative values arise around…
We suggest a two-dimensional wavelet devised to deduce the large-scale structure of a physical field (e.g., the Galactic magnetic field) from its integrals along straight paths from irregularly spaced data points to a fixed interior point…
An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having…
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
We present a novel method for predicting accurate depths from monocular images with high efficiency. This optimal efficiency is achieved by exploiting wavelet decomposition, which is integrated in a fully differentiable encoder-decoder…
We demonstrate how the image analysis technique of wavelet decomposition can be applied to the gamma-ray sky to separate emission on different angular scales. New structures on scales that differ from the scales of the conventional…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…