Related papers: Using fractional differentiation in astronomy
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
We address the problem of discretizing continuous cosmological signals such as a galaxy distribution for further processing with Fast Fourier techniques. Discretizing, in particular representing continuous signals by discrete sets of sample…
Speckle Imaging based on triple correlation is a very efficient image reconstruction technique which is used to retrieve Fourier phase information of the object in presence of atmospheric turbulence. We have developed both Direct Bispectrum…
One of the most challenging open questions in physics today is discovering the nature of dark matter. In this work we study the imaging formation in dark matter (DM) halos due to an external light source using some DM profiles for…
Fractional vector calculus is the building block of the fractional partial differential equations that model non-local or long-range phenomena, e.g., anomalous diffusion, fractional electromagnetism, and fractional advection-dispersion. In…
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…
Next generation probes of dark matter and dark energy require high precision reconstruction of faint galaxy shapes from hundreds of dithered exposures. Current practice is to stack the images. While valuable for many applications, this…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
Imaging the atmosphere using ground-based sky cameras is a popular approach to study various atmospheric phenomena. However, it usually focuses on the daytime. Nighttime sky/cloud images are darker and noisier, and thus harder to analyze.…
Coadded astronomical images are created by stacking multiple single-exposure images. Because coadded images are smaller in terms of data size than the single-exposure images they summarize, loading and processing them is less…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
Recently we put forward a framework where the dark matter (DM) component within virialized halos is subject to a non-local interaction originated by fractional gravity (FG) effects. In previous works we demonstrated that such a framework…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
The image subtraction method is a powerful tool to analyze the light variations in crowded fields. This method is able to achieve a nearly optimal differential photometry, even in very dense regions. However, image subtraction is not…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
One of the most useful techniques in astronomical instrumentation is image slicing. It enables a spectrograph to have a more compact angular slit, whilst retaining throughput and increasing resolving power. Astrophotonic components like the…
We review the current state of data mining and machine learning in astronomy. 'Data Mining' can have a somewhat mixed connotation from the point of view of a researcher in this field. If used correctly, it can be a powerful approach,…
This study introduces a novel unsupervised medical image feature extraction method that employs spatial stratification techniques. An objective function based on weight is proposed to achieve the purpose of fast image recognition. The…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…