Alternating-Direction Line-Relaxation Methods on Multicomputers

We study the multicom.puter performance of a three-dimensional Navier–Stokes solver based on alternating-direction line-relaxation methods. We compare several multicomputer implementations, each of which combines a particular line-relaxation method and a particular distributed block-tridiagonal solver. In our experiments, the problem size was determined by resolution requirements of the application. As a result, the granularity of the computations of our study is finer than is customary in the performance analysis of concurrent block-tridiagonal solvers. Our best results were obtained with a modified half-Gauss–Seidel line-relaxation method implemented by means of a new iterative block-tridiagonal solver that is developed here. Most computations were performed on the Intel Touchstone Delta, but we also used the Intel Paragon XP/S, the Parsytec SC-256, and the Fujitsu S-600 for comparison

First order algorithms in variational image processing

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow \min_u$ ; where the functional ${\cal D}$ is a data fidelity term also depending on some input data $f$ and measuring the deviation of $Ku$ from such and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear) forward operator modeling the dependence of data on an underlying image, and $\alpha$ is a positive regularization parameter. While ${\cal D}$ is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof or $\ell_1$-norms of coefficients arising from scalar products with some frame system. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. Here we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure

The Application of Preconditioned Alternating Direction Method of Multipliers in Depth from Focal Stack

Post capture refocusing effect in smartphone cameras is achievable by using focal stacks. However, the accuracy of this effect is totally dependent on the combination of the depth layers in the stack. The accuracy of the extended depth of field effect in this application can be improved significantly by computing an accurate depth map which has been an open issue for decades. To tackle this issue, in this paper, a framework is proposed based on Preconditioned Alternating Direction Method of Multipliers (PADMM) for depth from the focal stack and synthetic defocus application. In addition to its ability to provide high structural accuracy and occlusion handling, the optimization function of the proposed method can, in fact, converge faster and better than state of the art methods. The evaluation has been done on 21 sets of focal stacks and the optimization function has been compared against 5 other methods. Preliminary results indicate that the proposed method has a better performance in terms of structural accuracy and optimization in comparison to the current state of the art methods.Comment: 15 pages, 8 figure