Livia Marcellino

A smoothing spline that approximates Laplace transform functions only known on measurements on the real axis

The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has a finite set of data and one wants to recover an estimate of the inverse Laplace function from that. We propose a fitting model of data. More precisely, given a finite set of measurements on the real axis, arising from an unknown Laplace transform function, we construct a dth degree generalized polynomial smoothing spline, where d = 2m − 1, such that internally to the data interval it is a dth degree polynomial complete smoothing spline minimizing a regularization functional, and outside the data interval, it mimics the Laplace transform asymptotic behavior, i.e. it is a rational or an exponential function (the end behavior model), and at the boundaries of the data set it joins with regularity up to order m − 1, with the end behavior model. We analyze in detail the generalized polynomial smoothing spline of degree d = 3. This choice was motivated by the (ill)conditioning of the numerical computation which strongly depends on the degree of the complete spline. We prove existence and uniqueness of this spline. We derive the approximation error and give a priori and computable bounds of it on the whole real axis. In such a way, the generalized polynomial smoothing spline may be used in any real inversion algorithm to compute an approximation of the inverse Laplace function. Experimental results concerning Laplace transform approximation, numerical inversion of the generalized polynomial smoothing spline and comparisons with the exponential smoothing spline conclude the work.

Toward a Multi-level Parallel Framework on GPU Cluster with PetSC-CUDA for PDE-based Optical Flow Computation

In this work we present a multi-level parallel framework for the Optical Flow computation on a GPUs cluster, equipped with a scientific computing middleware (the PetSc library). Starting from a flow-driven isotropic method, which models the optical flow problem through a parabolic partial differential equation (PDE), we have designed a parallel algorithm and its software implementation that is suitable for heterogeneous computing environments (multiprocessor, single GPU and cluster of GPUs). The proposed software has been tested on real SAR images sequences. Numerical experiments highlight the performance of the proposed software framework, which can reach a gain of about 95% with respect to the sequential implementation.

Deconvolution of 3d fluorescence microscopy images using graphics processing units

We consider the deconvolution of 3D Fluorescence Microscopy RGB images, describing the benefits arising from facing medical imaging problems on modern graphics processing units (GPUs), that are non expensive parallel processing devices available on many up-to-date personal computers. We found that execution time of CUDA version is about 2 orders of magnitude less than the one of sequential algorithm. Anyway, the experiments lead some reflections upon the best setting for the CUDA-based algorithm. That is, we notice the need to model the GPUs architectures and their characteristics to better describe the performance of GPU-algorithms and what we can expect of them.

An error estimate of Gaussian recursive filter in 3Dvar problem

Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with a very large covariance matrix having Gaussian correlation structure. This operation may be interpreted as a Gaussian convolution, that is a very expensive numerical kernel. Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively applied in the meteorology, in the oceanography and in forecast models. In this paper, we deal with an oceanographic 3D-Var data assimilation scheme, named OceanVar, where the linear system is solved by using the Conjugate Gradient (GC) method by replacing, at each step, the Gaussian convolution with RFs. Here we give theoretical issues on the discrete convolution approximation with a first order (1st-RF) and a third order (3rd-RF) recursive filters. Numerical experiments confirm given error bounds and show the benefits, in terms of accuracy and performance, of the 3-rd RF.

Numerical solution of diffusion models in biomedical imaging on multicore processors

In this paper, we consider nonlinear partial differential equations (PDEs) of diffusion/advection type underlying most problems in image analysis. As case study, we address the segmentation of medical structures. We perform a comparative study of numerical algorithms arising from using the semi-implicit and the fully implicit discretization schemes. Comparison criteria take into account both the accuracy and the efficiency of the algorithms. As measure of accuracy, we consider the Hausdorff distance and the residuals of numerical solvers, while as measure of efficiency we consider convergence history, execution time, speedup, and parallel efficiency. This analysis is carried out in a multicore-based parallel computing environment.

A GPU parallel implementation of the Local Principal Component Analysis overcomplete method for DW image denoising

We focus on the Overcomplete Local Principal Component Analysis (OLPCA) method, which is widely adopted as denoising filter. We propose a programming approach resorting to Graphic Processor Units (GPUs), in order to massively parallelize some heavy computational tasks of the method. In our approach, we design and implement a parallel version of the OLPCA, by using a suitable mapping of the tasks on a GPU architecture with the aim to investigate the performance and the denoising features of the algorithm. The experimental results show improvements in terms of GFlops and memory throughput.

A parallel PDE-based numerical algorithm for computing the Optical Flow in hybrid systems

Abstract In this paper, we propose a fine-to-coarse parallelization strategy in order to exploit, in a case study, a parallel hybrid architecture. We consider the Optical Flow numerical problem, modelled by partial differential equations, and implement a parallel multilevel software. Our hybrid software solution is a smart combination between codes on Graphic Processor Units (GPUs) and standard scientific parallel computing libraries on a cluster. Numerical experiments, on real satellite image sequences coming from a large dataset in a big data scenario, together with application profiling, highlight good results in terms of performance for the proposed approach.

A Parallel Three‐dimensional Variational Data Assimilation Scheme

Data Assimilation (DA) refers to the methods for merging observed (generally sparse and noisy) information into the numerical model. Good assimilations make the modeled state more consistent with the observations. Effective data assimilation systems tend to make forecasts more accurate within the ability of the model. In this work we discuss some computational efforts towards the development of parallel three dimensional data assimilation scheme, based on the oceanographic 3D‐VAR assimilation scheme, named OCEANVAR.

A K-iterated scheme for the first-order Gaussian Recursive Filter with boundary conditions

Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively used in several research fields. When applied to signals with support in a finite domain, RFs can generate distortions and artifacts, mostly localized at the boundaries of the computed solution. To deal with this issue, heuristic and theoretical end conditions have been proposed in literature. However, these end conditions strategies do not consider the case in which a Gaussian RF is applied more than once, as often happens in several realistic applications. In this paper, we suggest a way to use the end conditions for such a K-iterated Gaussian RF and propose an algorithm that implements the described approach. Tests and numerical experiments show the benefit of the proposed scheme.

A GPU Algorithm in a Distributed Computing System for 3D MRI Denoising

An interesting challenge in E-health is to perform real-time diagnosis. In many distributed computing systems the data processing stage, generally assigned on standard computational CPU environments, is a critical aspect. In particular, the analysis of magnetic resonance imaging (MRI) for improving the quality of images and helping the diagnosis requires an high computational complexity. Using Graphics Processing Units (GPUs) on High Performance Computing (HPC), the images processing step can be accelerated by speeding the whole diagnosis procedure. In this paper, we propose a parallel algorithm, on a GPU environment, for MRI denoising in order to make the diagnostic system more efficient. As case study, we consider the Optimized Blockwise Non Local Means (OB-NLM) method. Its intrinsic nature makes it perfectly suited for parallelization and multithreading implementation, especially for GPUs architectures. The results show a significant improvement of the entire healthcare practice procedure in terms of performances.