Yi-Fei Pu

Fractional Differential Mask: A Fractional Differential-Based Approach for Multiscale Texture Enhancement

In this paper, we intend to implement a class of fractional differential masks with high-precision. Thanks to two commonly used definitions of fractional differential for what are known as Grumwald-Letnikov and Riemann-Liouville, we propose six fractional differential masks and present the structures and parameters of each mask respectively on the direction of negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal. Moreover, by theoretical and experimental analyzing, we demonstrate the second is the best performance fractional differential mask of the proposed six ones. Finally, we discuss further the capability of multiscale fractional differential masks for texture enhancement. Experiments show that, for rich-grained digital image, the capability of nonlinearly enhancing complex texture details in smooth area by fractional differential-based approach appears obvious better than by traditional integral-based algorithms.

Fractional Extreme Value Adaptive Training Method: Fractional Steepest Descent Approach

The application of fractional calculus to signal processing and adaptive learning is an emerging area of research. A novel fractional adaptive learning approach that utilizes fractional calculus is presented in this paper. In particular, a fractional steepest descent approach is proposed. A fractional quadratic energy norm is studied, and the stability and convergence of our proposed method are analyzed in detail. The fractional steepest descent approach is implemented numerically and its stability is analyzed experimentally.

A new CT metal artifacts reduction algorithm based on fractional-order sinogram inpainting

In this paper, we propose a new metal artifacts reduction algorithm based on fractional-order total-variation sinogram inpainting model for X-ray computed tomography (CT). The numerical algorithm for our fractional-order framework is also analyzed. Simulations show that, both quantitatively and qualitatively, our method is superior to conditional interpolation methods and the classic integral-order total variation model.

Efficient CT metal artifact reduction based on fractional-order curvature diffusion.

We propose a novel metal artifact reduction method based on a fractional-order curvature driven diffusion model for X-ray computed tomography. Our method treats projection data with metal regions as a damaged image and uses the fractional-order curvature-driven diffusion model to recover the lost information caused by the metal region. The numerical scheme for our method is also analyzed. We use the peak signal-to-noise ratio as a reference measure. The simulation results demonstrate that our method achieves better performance than existing projection interpolation methods, including linear interpolation and total variation.

A novel approach for multi-scale texture segmentation based on fractional differential

In this paper, we intend to implement multi-scale texture segmentation by fractional differential. We propose two fractional differential masks and present the structures and parameters of each mask, respectively, on eight directions. Moreover, by theoretical and experimental analysis, we find the better performance fractional differential mask. Finally, we further discuss the capability of fractional differential for multi-scale texture segmentation. Experiments show that, for rich-grained digital images, the capability for multi-scale texture segmentation by fractional differential-based approach appears efficient.

Improved DCT-Based Nonlocal Means Filter for MR Images Denoising

The nonlocal means (NLM) filter has been proven to be an efficient feature-preserved denoising method and can be applied to remove noise in the magnetic resonance (MR) images. To suppress noise more efficiently, we present a novel NLM filter based on the discrete cosine transform (DCT). Instead of computing similarity weights using the gray level information directly, the proposed method calculates similarity weights in the DCT subspace of neighborhood. Due to promising characteristics of DCT, such as low data correlation and high energy compaction, the proposed filter is naturally endowed with more accurate estimation of weights thus enhances denoising effectively. The performance of the proposed filter is evaluated qualitatively and quantitatively together with two other NLM filters, namely, the original NLM filter and the unbiased NLM (UNLM) filter. Experimental results demonstrate that the proposed filter achieves better denoising performance in MRI compared to the others.

A recursive two-circuits series analog fractance circuit for any order fractional calculus

The paper analyzes the fractional calculuss Caputo definition in time domain and Fourier transforms definition in frequency domain, then puts forward and discusses a 1/2order two-circuits series analog fractance circuit. On this bases, we further put forward and discusses a general recursive two-circuits series analog fractance circuit for any order fractional calculus. It is proved to performance correctly and efficiently by Computer simulation and circuit analog. At the same time, we probes the theoretical and engineering problems that need to be deeply researched in the area of the applications of fractional calculus to communication and information processing. The result educing by the paper is the basis for further theoretic research and engineering implement for structuring fractance circuit of any order fractional calculus.

Fractional partial differential equation denoising models for texture image

In this paper, a set of fractional partial differential equations based on fractional total variation and fractional steepest descent approach are proposed to address the problem of traditional drawbacks of PM and ROF multi-scale denoising for texture image. By extending Green, Gauss, Stokes and Euler-Lagrange formulas to fractional field, we can find that the integer formulas are just their special case of fractional ones. In order to improve the denoising capability, we proposed 4 fractional partial differential equation based multiscale denoising models, and then discussed their stabilities and convergence rate. Theoretic deduction and experimental evaluation demonstrate the stability and astringency of fractional steepest descent approach, and fractional nonlinearly multi-scale denoising capability and best value of parameters are discussed also. The experiments results prove that the ability for preserving high-frequency edge and complex texture information of the proposed denoising models are obviously superior to traditional integral based algorithms, especially for texture detail rich images.

Statistical iterative reconstruction using adaptive fractional order regularization.

In order to reduce the radiation dose of the X-ray computed tomography (CT), low-dose CT has drawn much attention in both clinical and industrial fields. A fractional order model based on statistical iterative reconstruction framework was proposed in this study. To further enhance the performance of the proposed model, an adaptive order selection strategy, determining the fractional order pixel-by-pixel, was given. Experiments, including numerical and clinical cases, illustrated better results than several existing methods, especially, in structure and texture preservation.

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron’s fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.