Related papers: Fractional differentiation based image processing

In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…

In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…

Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…

Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the…

We introduce some new forensics based on differential imaging, where a novel category of visual evidence created via subtle interactions of light with a scene, such as dim reflections, can be computationally extracted and amplified from an…

Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…

We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…

Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…

Motivated by the success of fractional pixel motion in video coding, we explore the design of motion estimation with fractional-voxel resolution for compression of color attributes of dynamic 3D point clouds. Our proposed block-based…

A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…

We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…

The recent theory of fractional $h$-difference equations introduced in [N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional variational problems, Signal Process. 91 (2011), no. 3, 513--524], is enriched with useful…

In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion…

The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis…

It is shown that calculus can apply on a fractal structure with the condition that the infinitesimal limit of change of the variable is larger than the lower cut-off of the fractal structure, and an assumption called local decomposability.…

A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel…

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…

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…

Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…

This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…