Related papers: Fractional Calculus In Image Processing: A Review
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
Image processing is one of the most immerging and widely growing techniques making it a lively research field. Image processing is converting an image to a digital format and then doing different operations on it, such as improving the…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
In this report, a de-hazing algorithm based on probability and multi-scale fractional order-based fusion is proposed. The proposed scheme improves on a previously implemented multiscale fraction order-based fusion by augmenting its local…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…
In this paper, complex-order derivative and integral filters are proposed, which are consistent with the filters with fractional derivative and integral orders. Compared with the filters designed only with real orders, complex order filters…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…
Farey sequence has been a topic of interest to the mathematicians since the very beginning of last century. With the emergence of various algorithms involving the digital plane in recent times, several interesting works related with the…
Image processing has always been a topic of significant importance to society. Recently, this field has gained considerable prominence due to the development of intelligent systems. In this work, we present a new method of image processing…
Numerical methods for fractional calculus attract increasing interests due to its wide applications in various fields such as physics, mechanics, etc. In this paper, we focus on constructing high-order algorithms for Riesz derivatives,…
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…
Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
The fractional order system, which is described by the fractional order derivative and integral, has been studied in many engineering areas. Recently, the concept of fractional order has been generalized to the distributed order concept,…
We define hyperbolic fractional-order Fourier transformations by replacing the circular trigonometric functions in the integral expressions of conventional fractional-order Fourier transformations with hyperbolic trigonometric functions. We…
System identification is a necessity in control theory. Classical control theory usually considers processes with integer order transfer functions. Real processes are usually of fractional order as opposed to the ideal integral order…
Image optimization problems encompass many applications such as spectral fusion, deblurring, deconvolution, dehazing, matting, reflection removal and image interpolation, among others. With current image sizes in the order of megabytes, it…
Modeling human operator's dynamic plays a very important role in the manual closed-loop control system, and it is an active research area for several decades. Based on the characteristics of human brain and behaviour, a new kind of…