Jiebao Sun

Adaptive Perona–Malik Model Based on the Variable Exponent for Image Denoising

This paper introduces a class of adaptive Perona-Malik (PM) diffusion, which combines the PM equation with the heat equation. The PM equation provides a potential algorithm for image segmentation, noise removal, edge detection, and image enhancement. However, the defect of traditional PM model is tending to cause the staircase effect and create new features in the processed image. Utilizing the edge indicator as a variable exponent, we can adaptively control the diffusion mode, which alternates between PM diffusion and Gaussian smoothing in accordance with the image feature. Computer experiments indicate that the present algorithm is very efficient for edge detection and noise removal.

A Doubly Degenerate Diffusion Model Based on the Gray Level Indicator for Multiplicative Noise Removal

Multiplicative noise removal is a challenging task in image processing. Inspired by the impressive performance of nonlinear diffusion models in additive noise removal, we address this problem in the view of nonlinear diffusion equation theories rather than the traditional variation methods. We develop a nonlinear diffusion filter denoising framework, which considers not only the information of the gradient of the image, but also the information of gray levels of the image. Furthermore, under this framework, we propose a doubly degenerate diffusion model for multiplicative noise removal, which is analyzed with respect to some of its properties and behavior in denoising process. In numerical aspects, we present an efficient scheme which uses a stabilization by fast explicit diffusion for the implementation of the multiplicative noise removal model. Finally, the experimental results illustrate effectiveness and efficiency of the proposed model.

A New Robust Watermarking Algorithm Based on DWT

Robustness is difficult to resolve in digital watermarking research, and contradicts its stealthiness. So the key of designing robust digital watermarking is selecting watermark embedding positions. Around these problems, we study the robust digital watermarking algorithm based on DWT. By wavelet transform, image smoothing based on PDE, and morphology operators (dilation and erosion), we obtain the relative low-frequency regions with small changing which can not be detected easily by human eyes, and then get the embedding positions. The watermark embedded in these positions has a proper consideration on both robustness and invisibility of the watermark. Experiments show that this algorithm is robust to JPEG2000 compression, also to JPEG compression, sharpening, salt and pepper noise, gama correction, a number of regular geometric attacks and other image processing operations.

Local existence and uniqueness of solutions of a degenerate parabolic system

This article deals with a degenerate parabolic system coupled with general nonlinear terms. Using the method of regularization and monotone iteration technique, we obtain the local existence of solutions to the Dirichlet initial boundary value problem. We also establish the uniqueness of the solution if the reaction terms satisfy the Lipschitz condition.

Asymptotic Behavior of Solutions of a Periodic Diffusion Equation

We consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method. Then by using Moser iterative technique and the method of contradiction, we establish the boundedness estimate of nonnegative periodic solutions, by which we show that the attraction of nontrivial nonnegative periodic solutions, that is, all non-trivial nonnegative solutions of the initial boundary value problem, will lie between a minimal and a maximal nonnegative nontrivial periodic solutions, as time tends to infinity.

A novel variational model for image segmentation

In this paper, we propose a new variational model for image segmentation. Our model is inspired by the complex Ginzburg-Landau model and the semi-norm defined by us. This new model can detect both the convex and concave parts of images. Moreover, it can also detect non-closed edges as well as quadruple junctions. Compared with other methods, the initialization is completely automatic and the segmented images obtained by using our new model could keep fine structures and edges of the original images very effectively. Finally, numerical results show the effectiveness of our model.

A non-divergence diffusion equation for removing impulse noise and mixed Gaussian impulse noise

In this paper, a non-divergence diffusion equation consisting of an impulse noise indicator λ and a regularized Perona-Malik (RPM) diffusion operator is proposed for the removal of impulse noise. The impulse noise indicator λ is designed to keep values of noise-free pixels unaltered while the Gaussian kernel in the RPM operator makes the proposed equation insensitive to impulse noise. As a result, the proposed equation succeeds in noise suppression as well as edge preserving and shows better performance than state-of-the-art PDE-based methods and variational regularization methods. In addition, the numerical solution of the proposed equation has a certain asymptotic behavior: it converges to the solution we are interested in automatically. This property avoids the problem of choosing a stopping time in numerical experiments and allows us to continue removing impulse noise and mixed Gaussian impulse noise by using the proposed equation.

Salt-and-Pepper Noise Removal via Local Hölder Seminorm and Nonlocal Operator for Natural and Texture Image

Utilizing local Hölder seminorm and nonlocal operator, we propose two efficient salt-and-pepper noise removal algorithms in this paper. We first minimize a local Hölder seminorm based functional which has a great capacity to restore natural images. Then by the definition of nonlocal operator, a new TV-based functional is proposed which inherits the advantage of nonlocal method and not only suppresses the noise but also restores the geometrical and texture features of noisy images. An alternative numerical scheme is also proposed to solve our functionals which reduces the computational complexity greatly. Experimental results are reported to compare the existing methods and demonstrate that the proposed algorithms are efficient even when the noise level is as high as 90 %.

An Image Level Set Method for Denoising

In this paper, we propose a new algorithm for image denoising. Our method based on image level set and partial differential equations (PDE) operator. The new method is feasible and easy to implement. Moreover, our method can also retain the key information and some fine structures of image. Compared with other traditional methods, our method can serve a definite purpose in reducing more types of noise (Gaussian, Poisson and Salt & Pepper noise). Finally, numerical results show the effectiveness of our method.

A new variational model for segmenting objects of interest from color images.

We propose a new variational model for segmenting objects of interest from color images. This model is inspired by the geodesic active contour model, the region-scalable fitting model, the weighted bounded variation model and the active contour models based on the Mumford-Shah model. In order to segment desired objects in color images, the energy functional in our model includes a discrimination function that determines whether an image pixel belongs to the desired objects or not. Compared with other active contour models, our new model cannot only avoid the usual drawback in the level set approach but also detect the objects of interest accurately. Moreover, we investigate the new model mathematically and establish the existence of the minimum to the new energy functional. Finally, numerical results show the effectiveness of our proposed model.