Zhichang Guo

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 Total Variation Model Based on the Strictly Convex Modification for Image Denoising

We propose a strictly convex functional in which the regular term consists of the total variation term and an adaptive logarithm based convex modification term. We prove the existence and uniqueness of the minimizer for the proposed variational problem. The existence, uniqueness, and long-time behavior of the solution of the associated evolution system is also established. Finally, we present experimental results to illustrate the effectiveness of the model in noise reduction, and a comparison is made in relation to the more classical methods of the traditional total variation (TV), the Perona-Malik (PM), and the more recent D-α-PM method. Additional distinction from the other methods is that the parameters, for manual manipulation, in the proposed algorithm are reduced to basically only one.

A Convex Adaptive Total Variation Model Based on the Gray Level Indicator for Multiplicative Noise Removal

This paper focuses on the problem of multiplicative noise removal. Using a gray level indicator, we derive a new functional which consists of the adaptive total variation term and the global convex fidelity term. We prove the existence, uniqueness, and comparison principle of the minimizer for the variational problem. The existence, uniqueness, and long-time behavior of the associated evolution equation are established. Finally, experimental results illustrate the effectiveness of the model in multiplicative noise reduction. Different from the other methods, the parameters in the proposed algorithms are found dynamically.

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 %.

Image Denoising via Nonlinear Hybrid Diffusion

A nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusion is nonlinear anisotropic and forward-backward. Unlike the Perona-Malik (PM) diffusion, the new forward-backward diffusion is adjustable and under control. Then, the existence, uniqueness, and long-time behavior of the new regularization equation of the model are established. Finally, using the explicit difference scheme (PM scheme) and implicit difference scheme (AOS scheme), we do numerical experiments for different images, respectively. Experimental results illustrate the effectiveness of the new model with respect to other known models.

A Linear Reaction-Diffusion System with Interior Degeneration for Color Image Compression

This paper considers colorization-based image compression in RGB color space. In compression, we store only the compressed luminance component of the original color image and a few representative pixels extracted from the original color image. In decompression, by explicitly introducing the relation between the luminance component and the original color image into diffusion equations, a linear reaction-diffusion system with Perona--Malik type diffusion coefficient is proposed to reconstruct R, G, and B channels simultaneously. The Perona--Malik type diffusion coefficient is a function of the luminance component and leads to interior degenerations, in general. It yields anisotropic smoothing in the restored color image and constrains the geometry of the restored image to follow the geometry of the luminance component. The existence and uniqueness of solutions for the proposed system with a specific class of diffusion coefficients are proved in a weighted Sobolev space. The selection of representative pixel...

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona–Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.

An image denoising model based on a fourth-order nonlinear partial differential equation

Abstract Image denoising is a challenging task in the fields of image processing and computer vision. Inspired by the good performance of nonlinear fourth-order models in recovering smooth region, we proposed a fourth-order image denoising model. Using the fixed point theorem, we established the existence and uniqueness of the entropy solution. Based on the fast explicit diffusion scheme (FED), numerical experiments illustrate the effectiveness of the suggested method in image denoising. The results have been compared with three famous fourth-order models, You and Kaveh (YK) model, Lysaker, Lundervold and Tai (LLT) model and the more recent mean curvature (MC) model. The proposed model has the superiority in terms of removing noise while preserving image features.