Chaos theory describes the dynamical systems which exhibit unpredictable, yet deterministic, behavior. Chaotic systems have a remarkable importance in both modeling and information processing in many fields. Fractional calculus has also become a powerful tool in describing the dynamics of complex systems such as fractional order (FO) chaotic systems. The FO parameter adds extra degrees of freedom which increases the design flexibility and adds more control on the design. The extra parameters increase the chaotic range. This chapter provides a review of several generalized discrete time one-dimensional maps. The generalizations include a signed control parameter, scaling parameters, and shaping parameters. The properties of the generalized fractional logistic map are presented. The generalized fractional tent map is presented and its properties are studied and validated using numerical simulations. Various simulations are conducted including time series, bifurcation diagrams, and various chaotic properties against the system parameters and FO parameter. © 2018 Elsevier Inc. All rights reserved.
A novel image encryption system merging fractional-order edge detection and generalized chaotic maps
This paper presents a novel lossless image encryption algorithm based on edge detection and generalized chaotic maps for key generation. Generalized chaotic maps, including the fractional-order, the delayed, and the Double-Humped logistic maps, are used to design the pseudo-random number key generator. The generalization parameters add extra degrees of freedom to the system and increase the keyspace achieving more secure keys. Fractional order edge detection filters exhibited better noise robustness than the conventional integer-order ones, rendering the system to be suitable for medical imaging security. The proposed system flexibly integrate different edge detectors, as well as various logistic maps for key generation. The sensitivity of the chaotic maps to all parameters guarantees the encryption system key sensitivity. Security analyses aspects assure the efficiency of the proposed algorithm performance, having high pixel correlation coefficients and flat histograms of cipher images reported. A comparison between the proposed scheme with existing cryptosystems is also presented, regarding histogram uniformity, contrast analysis, Shannon entropy measurements. Compared to the state of the art algorithms, the proposed algorithm has higher statistical and cryptanalytic properties. © 2019
Reconfigurable hardware implementation of K-nearest neighbor algorithm on FPGA
Nowadays, Machine Learning is commonly integrated into most daily life applications in various fields. The K Nearest Neighbor (KNN), which is a robust Machine Learning algorithm, is traditionally used in classification tasks for its simplicity and training-less nature. Hardware accelerators such as FPGAs and ASICs are greatly needed to meet the increased requirements of performance for these applications. It is well known that ASICs are non-programmable and only fabricated once with high expenses, this makes the fabrication of a complete chip for a specific classification problem inefficient. As a better alternative to this challenge, in this work, a reconfigurable hardware architecture of the KNN algorithm is proposed where the employed dataset, the algorithm parameters, and the distance metric used to evaluate the nearest neighbors are all updatable after fabrication, in the ASIC case, or after programming, in the FPGA case. The architecture is also made flexible to accommodate different memory requirements and allow variable arithmetic type and precision selection. Both parameters can be adjusted before fabrication to account only for the expected memory requirement and the fixed point precision required or floating point arithmetic if needed. The proposed architecture is realized on the Genesys 2 board based on Xilinx’s Kintex-7 FPGA. The results obtained from the experiment are consistent with those obtained from the simulation and software analysis. The proposed realization reaches a frequency of up to around 110 MHz and a power consumption of less than 0.4 watts © 2023 Elsevier GmbH
Optimization of Double fractional-order Image Enhancement System
Image enhancement is a vital process that serves as a tool for improving the quality of a lot of real-life applications. Fractional calculus can be utilized in enhancing images using fractional order kernels, adding more controllability to the system, due to the flexible choice of the fractional order parameter, which adds extra degrees of freedom. The proposed system merges two fractional order kernels which helps in image enhancement techniques, and the contribution of this work is based on the study of how to optimize this process. The optimization of the two fractional kernels was done using the neural network optimization algorithm (NNA) to utilize the best order for the two kernels. In this paper, three fractional kernels are studied to highlight the performance of image enhancement using fractional kernels against different metrics. Furthermore, three different combinations of two kernels are combined and studied to enhance the metrics score by utilizing two different fractional orders for each kernel. Various optimization algorithms are used to obtain the optimum fractional order for both single and combined kernels. Using the constrained NNA, the evaluation metrics of the image enhancement show a 33% increase in measure of enhancement metric (EME), 21% increase in contrast, and 4% increase in average gradient compared to the best-achieved metrics by the literature while keeping the similarity metric above 0.75. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
On The Optimization of Fractional Order Low-Pass Filters
This paper presents three different optimization cases for normalized fractional order low-pass filters (LPFs) with numerical, circuit and experimental results
Generalized fractional logistic map encryption system based on FPGA
This paper introduces the design of a generalized fractional order logistic map suitable for pseudorandom number key generators and its application in an encryption system based on FPGA
Generalized double-humped logistic map-based medical image encryption
This paper presents the design of the generalized Double Humped (DH) logistic map, used for pseudo-random number key generation (PRNG)
Fractional-order edge detection masks for diabetic retinopathy diagnosis as a case study
Edge detection is one of the main steps in the image processing field, especially in bio-medical imaging, to diagnose a disease or trace its progress