Related papers: Wavelet-based cross-correlation analysis of struct…
The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence…
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…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…
The mark weighted correlation function (MCF) $W(s,\mu)$ is a computationally efficient statistical measure which can probe clustering information beyond that of the conventional 2-point statistics. In this work, we extend the traditional…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
Ultrametric structure of the energy cascade process in a dynamical model of turbulence is studied. The tree model we use can be viewed as an approximated one-dimensional truncation of the wavelets resolved Navier-Stokes dynamics. Varying…
Low-dose Positron Emission Tomography (PET) imaging reduces patient radiation exposure but suffers from increased noise that degrades image quality and diagnostic reliability. Although diffusion models have demonstrated strong denoising…
We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant…
The universality of interstellar turbulence is examined from observed structure functions of 27 giant molecular clouds and Monte Carlo modeling. We show that the structure functions, dv=v0 l^gamma, derived from wide field imaging of CO…
We study an effect of large-scale coherent structures on global properties of turbulent convection in laboratory experiments in air flow in a rectangular chamber with aspect ratios $A \approx 2$ and $A\approx 4$ (with the Rayleigh numbers…
Understanding the evolving dependence between two clusters of multivariate signals is fundamental in neuroscience and other domains where sub-networks in a system interact dynamically over time. Despite the growing interest in multivariate…
The structure of molecular clouds (MCs) holds important clues on the physical processes that lead to their formation and subsequent evolution. While it is well established that turbulence imprints a self-similar structure to the clouds,…
Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, formation and dissipation of thin current sheets, stochastic heating. It is now…
We consider the 2D wavelet transform with two scales to study sky maps of temperature anisotropies in the cosmic microwave background radiation (CMB). We apply this technique to simulated maps of small sky patches of size 12.8 \times 12.8…
Coherent structures in two-dimensional Navier-Stokes turbulence are ubiquitously observed in nature, experiments and numerical simulations. The present study conducts a comparison between several structure detection schemes based on the…
Turbulence is a complex system exhibiting both universal statistical features and prominent coherent structures. We model turbulence using coherent vortices distributed within a multi-scale statistical framework, termed `woven turbulence'.…
We use the Gigaparsec WiggleZ (GiggleZ) simulations to characterise galaxy bias and its scale dependence for a range of redshifts and halo masses in a standard $\Lambda$LCDM cosmology. Assuming bias converges to a scale independent form at…
Texture classification is an important and challenging problem in many image processing applications. While convolutional neural networks (CNNs) achieved significant successes for image classification, texture classification remains a…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
Both pixel-based scale saliency (PSS) and basis project methods focus on multiscale analysis of data content and structure. Their theoretical relations and practical combination are previously discussed. However, no models have ever been…