000			07722nam a22002657a 4500
008			201210b2024 a|||f bm|| 00| 0 eng d
024	7		_2ORCID _a0000-0002-7567-6203
040			_aEG-CaNU _cEG-CaNU
041	0		_aeng _beng _bara
082			_a621
100	0		_aAlaa AbdAlrhman Mohammed _93230
245	1		_aFractional Calculus Based Image Simplification Algorithm For Medical applications _c/Alaa AbdAlrhman Mohammed
260			_c2024
300			_a p. _bill. _c21 cm.
500			_3Supervisor: Ahmed G. Radwan
502			_aThesis (MS.c)—Nile University, Egypt, 2024.
504			_a"Includes bibliographical references"
505	0		_aContents: Contents Page V List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVII List of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XX Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX Acknowledgment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXII Chapters: 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Thesis Motivation and Concepts of Review . . . . . . . . . . . . . . . . 5 2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Fractional Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Fractional Operator based on GL definition . . . . . . . . . 8 2.2.2 Fractional Operator based on RL Definition . . . . . . . . . 10 2.2.3 Fractional Operator Based on Deformable Definition . . . . 13 2.3 Image Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Fractional Kernels . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Anisotropic Diffusion Filters . . . . . . . . . . . . . . . . . . . . . . 21 2.4.1 Hardware Implementation of Anisotropic Filters on FPGA Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4.2 Pixel buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4.3 Kernel convolution . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.4 G function . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. New Implementation of GL-based Fractional Operator. 28 3.1 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1.1 Average fixed window optimization method . . . . . . . . . . 28 3.1.2 Optimum α method . . . . . . . . . . . . . . . . . . . . . . . 29 3.1.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 30 3.1.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 An Improved Approximation of GL Fractional Integral . . . . . . . . 33 3.2.1 Mathematical Analysis . . . . . . . . . . . . . . . . . . . . . . 33 3.2.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.3 Fixed window method . . . . . . . . . . . . . . . . . . . . . . 35 3.2.4 Quadratic approximation method . . . . . . . . . . . . . . . . 35 3.2.5 PWL approximation method . . . . . . . . . . . . . . . . . . . 36 3.2.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 38 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4. Hardware Accelerator of Fractional-order Derivative/Integral Operator based on Phase Optimized Filters with Applications 41 4.1 Filters Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.1 Proposed Phase Optimized FIR . . . . . . . . . . . . . . . . . 41 VI 4.1.2 Proposed Phase Optimized IIR . . . . . . . . . . . . . . . . . 44 4.2 FPGA Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4.1 Heaviside . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4.2 Edge Detection . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5. Application: Fractional based Image Processing 56 5.1 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2 Fractional Image Enhancement . . . . . . . . . . . . . . . . . . . . . 57 5.2.1 Double Fractional Kernel System . . . . . . . . . . . . . . . . 57 5.2.2 Fractional Kernels Optimization . . . . . . . . . . . . . . . . . 58 5.2.3 Single fractional kernels optimization . . . . . . . . . . . . . . 59 5.2.4 Double fractional kernels system optimization . . . . . . . . . 61 5.2.5 Constrained Double Optimization . . . . . . . . . . . . . . . . 62 5.3 Fractional Anisotropic Diffusion Filter . . . . . . . . . . . . . . . . . 66 5.3.1 Fractional Gradient Operator . . . . . . . . . . . . . . . . . . 67 5.3.2 Anisotropic Filter Design . . . . . . . . . . . . . . . . . . . . . 68 5.3.3 Optimizing Fractional Anisotropic Filter . . . . . . . . . . . . 72 5.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6. Conclusion and Future Work 79 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 VII Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Appendices: A. Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
520	3		_aAbstract: Fractional calculus is a powerful mathematical tool used to describe complex systems in physics, engineering, and finance. However, implementing fractional order systems in hardware can be resource-intensive, requiring large amounts of memory and processing power. Field programmable gate arrays (FPGAs) provide a platform for implementing fractional order systems that can conduct logic in parallel, resulting in faster and more efficient processing. This thesis proposes three new fractional order implementation methods that improve accuracy and reduce resource requirements. The results show that the proposed methods offer significant improvements in accuracy, power, latency, memory-units usage and DSPs compared to traditional methods. This thesis also proposes a soft IP library for different fractional operators implementation methods that can be included in FPGA different applications. In addition to exploring new implementation methods, this thesis investigates the use of fractional calculus in image enhancement and image simplification. The proposed methods are evaluated using metrics such as peak signal-to-noise ratio (PSNR) and the average gradient metric (AG) to determine their effectiveness. Overall, this thesis makes significant contributions to the field of fractional calculus, that can be of value in many fields. The proposed implementation methods and X image processing techniques can be used in a wide range of applications, including control systems, signal processing, and image processing. Keywords Fractional Calculus, FPGA, Matlab, Image Processing, Portable Devices, Anisotropic Filters, Grünwald–Letnikov, GA, FPA
546			_aText in English, abstracts in English and Arabic
650		4	_aMSD _9317
655		7	_2NULIB _aDissertation, Academic _9187
690			_aMSD _9317
942			_2ddc _cTH
999			_c10292 _d10292