Image denoising is still a challenging problem, particularly when the noise is made combining Gaussian noise and random-valued impulses. This article is concerned with diffusion-based denoising methods which can suppress such complicated noises effectively, preserving fine structures. We introduce a novel impulse-mowing anisotropic diffusion (IMAD) filter to cut out impulses and local maxima/minima without affecting surrounding pixel values. It has been numerically verified that the suggested mean filter carries out both mowing impulses and restoring fine structures satisfactorily. It outperforms nonlinear median filters, measured in PSNR and visual inspection.

This article is concerned with an effective PDE-based image zooming method which is an improvement of the so-called curvature interpolation method (CIM) previously developed in [H. Kim, Y. Cha, and S. Kim, IEEE Trans. Image Process., 20 (2011), pp. 1895--1903]. The new algorithm incorporates an iterative application of the CIM in order to be an interpolator and to construct a reliable image surface utilizing a generalized curvature source term estimated from the low resolution image. It also employs an effective 9-point scheme for the curvature evaluation which in turn makes the constructed image surface involve no observable ringing artifacts. It has been experimentally verified that the new method results in a high resolution image of clear and sharp edges and cloudless textures, showing qualities of superresolution. Its convergence is analyzed; various results are given to show effectiveness and reliability of the new method. The proposed method has proved not only superior to state-of-the-art methods in image quality but also sufficiently efficient to be applicable for real-time image zooming of arbitrary magnification factors.

We introduce a novel image zooming algorithm, called the curvature interpolation method (CIM), which is partial-differential-equation (PDE)-based and easy to implement. In order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect, the CIM first evaluates the curvature of the low-resolution image. After interpolating the curvature to the high-resolution image domain, the CIM constructs the high-resolution image by solving a linearized curvature equation, incorporating the interpolated curvature as an explicit driving force. It has been numerically verified that the new zooming method can produce clear images of sharp edges which are already denoised and superior to those obtained from linear methods and PDE-based methods of no curvature information. Various results are given to prove effectiveness and reliability of the new method.

This paper proposes a new interpolation method, called the error-amended sharp edge (EASE) scheme, which is a modified bilinear method. In order to remove/reduce interpolation artifacts such as image blur and the checkerboard effect (ringing), EASE tries to amend the interpolation error by employing the classical interpolation error theorem in an edge-adaptive fashion. EASE is applied for image zooming by both integer and noninteger magnification factors. The new interpolation scheme has proved to result in high-resolution images having clearer and sharper edges than linear interpolation methods, for all synthetic and natural images we have tested. EASE can be implemented with ease; it turns out to be similarly efficient as cubic interpolation schemes.

This article proposes a new interpolation method, called the error-amended sharp edge (EASE) scheme. EASE is a modified bilinear method which tries to amend the interpolation error in an edge-adaptive way by employing the interpolation error theorem. The resulting scheme has proved to result in zoomed images having sharper edges than bilinear, C1-bicubic, and C2-bicubic interpolation methods. EASE is similarly efficient as cubic interpolation methods and can be implemented with ease.

We propose a new model for image denoising which is a hybrid of the total variation model and the Laplacian mean-curvature model. An efficient numerical procedure to compute the hybrid model is also presented. The hybrid model and its computational procedure introduce a number of parameters. As a preliminary step to the synthesis of a method for selecting optimal parameters, the hybrid model was simulated on a number of known images with synthetically added noise. The parallel simulation code was easily composed from existing serial code and a dynamic load balancing tool. The estimated parallel efficiency of the simulation is in excess of 96% on 32 processors of a general-purpose Linux cluster.

This paper introduces edge-forming schemes for image zooming of color images by general magnification factors. In order to remove/reduce artifacts arising in image interpolation, such as image blur and the checkerboard effect, an edge-forming method is suggested to be applied as a postprocess of standard interpolation methods. The method is based on nonconvex nonlinear partial differential equations. The equations are carefully discretized, incorporating numerical schemes of anisotropic diffusion, to be able to form reliable edges satisfactorily. The alternating direction implicit (ADI) method is employed for an efficient simulation of the model. It has been numerically verified that the resulting algorithm can form clear edges in 2 to 3 ADI iterations. Various results are given to show th eeffectiveness and reliability of the algorithm.

The paper is concerned with PDE-based image restoration. A new model is introduced by hybridizing a nonconvex variant of the total variation minimization (TVM) and the motion by mean curvature (MMC) in order to deal with the mixture of the impulse and Gaussian noises reliably. We suggest the essentially nondissipative (ENoD) difference schemes for the MMC component to eliminate the impulse noise with a minimum (ideally no) introduction of dissipation. The MMC-TVM hybrid model and the ENoD schemes are applied for both gray-scale and color images. For color image denoising, we consider the chromaticity-brightness decomposition with the chromaticity formulated in the angle domain. An incomplete Crank-Nicolson alternating direction implicit time-stepping procedure is adopted to solve those differential equations efficiently. Numerical experiments have shown that the new hybrid model and the numerical schemes can remove the mixture of the impulse and Gaussian noises, efficiently and reliably, preserving edges quite satisfactorily.