Related papers: Using Wavelet Decomposition to Determine the Dimen…
The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a…
We present the first application of the Wavelet Scattering Transform (WST) in order to constrain the nature of gravity using the three-dimensional (3D) large-scale structure of the universe. Utilizing the Quijote-MG N-body simulations, we…
The large side aperture of the NuSTAR telescope for unfocused photons (so-called stray light) is a known source of rich astrophysical information. To support many studies based on the NuSTAR stray light data, we present a fully automatic…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show…
Continuous wavelet analysis has been increasingly employed in various fields of science and engineering due to its remarkable ability to maintain optimal resolution in both space and scale. Here, we introduce wavelet-based statistics,…
Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a…
We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the…
The influence of large-scale density fluctuations on structure formation on small scales is described by the three-point correlation function (bispectrum) in the so-called "squeezed configurations," in which one wavenumber, say $k_3$, is…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
Motivated by the existence problem of Fourier frames on fractal measures, we introduce Bessel and frame measures for a given finite measure on $\br^d$, as extensions of the notions of Bessel and frame spectra that correspond to bases of…
Weak lensing provides a direct measure of the distribution of mass in the universe, and is therefore a uniquely powerful probe of dark matter. Weak lensing can also be used to measure the twin phenomenon of dark energy, via its effect upon…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
O(N) methods are based on the decay properties of the density matrix in real space, an effect sometimes refered to as near-sightedness. We show, that in addition to this near-sightedness in real space there is also a near-sightedness in…
Two approaches (micro- and macro- investigations) are used to determine the dimension dependences of the optical parameters of the nanometer-scale layers of materials. It is shown that both an index of refraction and coefficient of…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an…
A giant planet embedded in a protoplanetary disk creates a gap. This process is important for both theory and observations. Using results of a survey for a wide parameter range with two-dimensional hydrodynamic simulations, we constructed…
Massive neutrinos influence the background evolution of the Universe as well as the growth of structure. Being able to model this effect and constrain the sum of their masses is one of the key challenges in modern cosmology. Weak-lensing…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…