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The particle-mesh method (PMM) is a powerful computational tool for the simulation of convection-dominated diffusion flows. The method introduces computational particles each of which is given a finite size and represents a large number of physical particles with the same properties. The convection part of the flow can be solved by moving the computational particles along the characteristics, while the diffusion part is carried out by utilizing a heat solver on a regular mesh. However, the method in practical applications shows the so-called ringing instability, an amplitude fluctuation in the computed solution. In this article, we suggest a new numerical technique of particle movement, called the dual-mesh characteristics (DMC) of which the second mesh is formed by tracking back the cells along the characteristics. The particle movement is carried out by interpreting the particle positions (in the previous time level) in terms of the multilinear coordinates of the second mesh. Strategies for the average ...

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.

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 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.

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 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 presents an efficient PDE-based interpolation algorithm for image super resolution (SR). Conventional PDE-based interpolation methods can produce sharp edges; however, they are approximators and tend to weaken fine structures. In order to overcome the drawback, a texture enhancement method is incorporated as a post-process of PDE-based interpolation methods. The post-process turns out to make the resulting algorithm an interpolator. It has been numerically verified that the resulting algorithm restores sharp edges and enhances fine structures satisfactorily, outperforming traditional methods. The suggested algorithm has also proved efficient enough to be applicable for real-time processing for resolution enhancement of images and video clips that are downloaded through internet connections or wireless communications. Numerical examples are shown to verify the claim.

We have developed a dental tomosynthesis system that is capable of being used for planning an implant procedure with much reduced patient dose. The system employs simple isocentric linear motion. The reconstruction algorithm is based on the backprojection filtering method in which incorporates apodizing filters to reduce blur artifacts originating from the out- of-planes and control high-frequency noise. For the volumetric imaging, we have synthesized two volume-data sets which are separately obtained from two different scans in angle. The reconstructed images for a skull phantom with the developed system demonstrate the potential use in dental imaging application with much reduced patient dose.

This article is concerned with a level set segmentation (active contour) algorithm for medical imagery. Due to difficulties such as noise and unclear edges, it is often challenging to obtain a reliable segmentation for medical images. In addition to introducing a new hybrid model which combines a gradient-based model and the Mumford-Shah (gradient-free) method, we study the so-called method of background subtraction (MBS) in order to improve reliability of the new model. A linearized alternating direction implicit method is applied for an efficient time integration. For a fast convergence, we also suggest effective initialization strategies for the level set function. The resulting algorithm has proved to locate the desired edges in 2-4 iterations.

In tomographic image processing of seismic data, the first-arrival traveltime (FATT) is often different from those of more energetic wavefronts in realistic media. Since the traveltime of most-energetic wavefront (METT) dominates the data, computing the METT is recognized as an essential element in modern seismic imaging techniques. Solving the full wave equation is extremely expensive to be impractical even for large-size computers to carry out; the solution of the eikonal equation for which the corresponding amplitude is continuous is conjectured to be the METT.