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.

Image denoising processes often lead to significant loss of fine structures such as edges and textures. This paper studies various innovative mathematical and numerical methods applicable for conventional PDE-based denoising models. The method of diffusion modulation is considered to effectively minimize regions of undesired excessive dissipation. Then we introduce a novel numerical technique for residual-driven constraint parameterization, in order for the resulting algorithm to produce clear images whose corresponding residual is as free of image textures as possible. A linearized Crank-Nicolson alternating direction implicit time-stepping procedure is adopted to simulate the resulting model efficiently. Various examples are presented to show efficiency and reliability of the suggested methods in image denoising.

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.

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