Jiliu Zhou

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.

Low-dose CT via convolutional neural network

In order to reduce the potential radiation risk, low-dose CT has attracted an increasing attention. However, simply lowering the radiation dose will significantly degrade the image quality. In this paper, we propose a new noise reduction method for low-dose CT via deep learning without accessing original projection data. A deep convolutional neural network is here used to map low-dose CT images towards its corresponding normal-dose counterparts in a patch-by-patch fashion. Qualitative results demonstrate a great potential of the proposed method on artifact reduction and structure preservation. In terms of the quantitative metrics, the proposed method has showed a substantial improvement on PSNR, RMSE and SSIM than the competing state-of-art methods. Furthermore, the speed of our method is one order of magnitude faster than the iterative reconstruction and patch-based image denoising methods.

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.

A Novel Image Denoising Algorithm Based on Riemann-Liouville Definition

In this paper, a novel image denoising algorithm named fractional integral image denoising algorithm (FIIDA) is proposed, which based on fractional calculus Riemann-Liouville definition. The structures of n*n fractional integral masks of this algorithm on the directions of 135 degrees, 90 degrees, 45 degrees, 0 degrees, 180 degrees, 315 degrees, 270 degrees and 225 degrees are constructed and discussed. The denoising performance of FIIDA is measured using experiments according to subjective and objective standards of visual perception and PSNR values. The simulation results show that the FIIDAs performance is prior to the Gaussian smoothing filter, especially when the noise standard deviation is less than 30.

Few-view image reconstruction with fractional-order total variation

This work presents a novel computed tomography (CT) reconstruction method for the few-view problem based on fractional calculus. To overcome the disadvantages of the total variation minimization method, we propose a fractional-order total variation-based image reconstruction method in this paper. The presented model adopts fractional-order total variation instead of traditional total variation. Different from traditional total variation, fractional-order total variation is derived by considering more neighboring image voxels such that the corresponding weights can be adaptively determined by the model, thus suppressing the over-smoothing effect. The discretization scheme of the fractional-order model is also given. Numerical and clinical experiments demonstrate that our method achieves better performance than existing reconstruction methods, including filtered back projection (FBP), the total variation-based projections onto convex sets method (TV-POCS), and soft-threshold filtering (STH).

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.

Few-view image reconstruction combining total variation and a high-order norm

This work presents a novel computed tomography reconstruction method for few‐view problem based on a compound method. To overcome the disadvantages of total variation (TV) minimization method, we use a high‐order norm coupled within TV and the numerical scheme for our method is given. We use the root mean square error as a referee. The numerical experiments demonstrate that our method achieves better performance than existing reconstruction methods, including filtered back projection, expectation maximization, and TV with projection on convex sets.

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.

A self-adaptive image normalization and quaternion PCA based color image watermarking algorithm

This paper proposes a novel robust digital color image watermarking algorithm which combines color image feature point extraction, shape image normalization and QPCA (quaternion principal component algorithm) based watermarking embedding (QWEMS) and extraction (QWEXS) schemes. The feature point extraction method called Mexican Hat wavelet scale interaction is used to select the points which can survive various attacks and also be used as reference points for both watermarking embedding and extraction. The normalization shape image of the local quadrangle image of which the four corners are feature points of the original image is invariant to translation, rotation, scaling and skew, by which we can obtain the relationship between the feature images of the original image and the watermarked image which has suffered with geometrical attacks. The proposed QWEMS and QWEXS schemes which denote the color pixel as a pure quaternion and the feature image as a quaternion matrix can improve the robustness and the imperceptibility of the embedding watermarking. To simplify the eigen-decomposition procedure of the quaternion matrix, we develop a calculation approach with which the eigen-values and the corresponding eigen-vectors of the quaternion matrix can be computed. A binary watermark image is embedded in the principal component coefficients of the feature image. Simulation results demonstrate that the proposed algorithm can survive a variety of geometry attacks, i.e. translation, rotation, scaling and skew, and can also resist the attacks of many signal processing procedures, for example, moderate JPEG compression, salt and pepper noise, Gaussian filtering, median filtering, and so on.