3,717 research outputs found
Astronomical image processing based on fractional calculus: the AstroFracTool
The implementation of fractional differential calculations can give new
possibilities for image processing tools, in particular for those that are
devoted to astronomical images analysis. As discussed in arxiv:0910.2381, the
fractional differentiation is able to enhance the quality of images, with
interesting effects in edge detection and image restoration. Here, we propose
the AstroFracTool, developed to provide a simple yet powerful enhancement
tool-set for astronomical images. This tool works evaluating the fractional
gradient of an image map. It can help produce an output image useful for
further research and scientific purposes, such as the detection of faint
objects and galaxy structures, or, in the case of planetary studies, the
enhancement of surface details.Comment: Keywords: Fractional calculation, image processing, astronom
Towards the Formalization of Fractional Calculus in Higher-Order Logic
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 analyze a wide class of physical systems in various fields of science and
engineering. In this paper, we describe an ongoing project which aims at
formalizing the basic theories of fractional calculus in the HOL Light theorem
prover. Mainly, we present the motivation and application of such formalization
efforts, a roadmap to achieve our goals, current status of the project and
future milestones.Comment: 9 page
A Robust Variable Step Size Fractional Least Mean Square (RVSS-FLMS) Algorithm
In this paper, we propose an adaptive framework for the variable step size of
the fractional least mean square (FLMS) algorithm. The proposed algorithm named
the robust variable step size-FLMS (RVSS-FLMS), dynamically updates the step
size of the FLMS to achieve high convergence rate with low steady state error.
For the evaluation purpose, the problem of system identification is considered.
The experiments clearly show that the proposed approach achieves better
convergence rate compared to the FLMS and adaptive step-size modified FLMS
(AMFLMS).Comment: 15 pages, 3 figures, 13th IEEE Colloquium on Signal Processing & its
Applications (CSPA 2017
Using fractional differentiation in astronomy
In a recent paper, published at arXiv:0910.2381, we started a discussion on
the new possibilities arising from the use of fractional differential calculus
in image processing. We have seen that the fractional calculation is able to
enhance the quality of images, with interesting possibilities in edge detection
and image restoration. Here, we want to discuss more deeply its role as a tool
for the processing of astronomical images. In particular, the fractional
differentiation can help produce a 'content-matter' based image from a pretty
astronomical image that can be used for more research and scientific purposes,
for instance to reveal faint objects galactic matter, nebulosity, more stars
and planetary surface detail
Simultaneous denoising and enhancement of signals by a fractal conservation law
In this paper, a new filtering method is presented for simultaneous noise
reduction and enhancement of signals using a fractal scalar conservation law
which is simply the forward heat equation modified by a fractional
anti-diffusive term of lower order. This kind of equation has been first
introduced by physicists to describe morphodynamics of sand dunes. To evaluate
the performance of this new filter, we perform a number of numerical tests on
various signals. Numerical simulations are based on finite difference schemes
or Fast and Fourier Transform. We used two well-known measuring metrics in
signal processing for the comparison. The results indicate that the proposed
method outperforms the well-known Savitzky-Golay filter in signal denoising.
Interesting multi-scale properties w.r.t. signal frequencies are exhibited
allowing to control both denoising and contrast enhancement
Liver CT enhancement using Fractional Differentiation and Integration
In this paper, a digital image filter is proposed to enhance the Liver CT image for improving the classification of tumors area in an infected Liver. The enhancement process is based on improving the main features within the image by utilizing the Fractional Differential and Integral in the wavelet sub-bands of an image. After enhancement, different features were extracted such as GLCM, GRLM, and LBP, among others. Then, the areas/cells are classified into tumor or non-tumor, using different models of classifiers to compare our proposed model with the original image and various established filters. Each image is divided into 15x15 non-overlapping blocks, to extract the desired features. The SVM, Random Forest, J48 and Simple Cart were trained on a supplied dataset, different from the test dataset. Finally, the block cells are identified whether they are classified as tumor or not. Our approach is validated on a group of patients’ CT liver tumor datasets. The experiment results demonstrated the efficiency of enhancement in the proposed technique
Image Inpainting and Enhancement using Fractional Order Variational Model
The intention of image inpainting is to complete or fill the corrupted or missing zones of an image by considering the knowledge from the source region. A novel fractional order variational image inpainting model in reference to Caputo definition is introduced in this article. First, the fractional differential, and its numerical methods are represented according to Caputo definition. Then, a fractional differential mask is represented in 8-directions. The complex diffusivity function is also defined to preserve the edges. Finally, the missing regions are filled by using variational model with fractional differentials of 8-directions. The simulation results and analysis display that the new model not only inpaints the missing regions, but also heightens the contrast of the image. The inpainted images have better visual quality than other fractional differential filters
- …