PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer

<div>Represented by the kernelized expectation maximization (KEM), the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration number. Also, it is generally difficult to simultaneously reduce image variance and preserve image details using kernels. To solve these problems, this paper presents a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smoothes the kernel coefficients, a non-convex kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that guarantees the convexity of composite regularizer. These kernel space regularizers are based on the theory of data manifold and graph regularization and can be constructed from different prior image data for simultaneous image variance reduction and image detail preservation. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.</div>

PET Image Reconstruction with Kernel and Kernel Space Composite Regularizer

<div>Represented by the kernelized expectation maximization (KEM), the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration number. Also, it is generally difficult to simultaneously reduce image variance and preserve image details using kernels. To solve these problems, this paper presents a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smoothes the kernel coefficients, a non-convex kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that guarantees the convexity of composite regularizer. These kernel space regularizers are based on the theory of data manifold and graph regularization and can be constructed from different prior image data for simultaneous image variance reduction and image detail preservation. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.</div>

PERBANDINGAN KERNEL SUPPORT VECTOR MACHINE (SVM) DALAM PENERAPAN ANALISIS SENTIMEN VAKSINISASI COVID-19

In early 2020, the first recorded death from the COVID-19 virus in China [3]. Followed by WHO which later stated that the COVID-19 virus caused a pandemic. Various efforts were made to minimize the transmission of COVID-19, such as physical distancing and large-scale social circulation. However, this resulted in a paralyzed economy, many factories or business shops closed, eliminating the livelihoods of many people. Vaccines may be a solution, various International Research Communities have conducted research on the COVID-19 vaccine. In early 2021 the Sinovac vaccine from China arrived in Indonesia and was declared a BPOM clinical trial, but the existence of the vaccine still raises pros and cons, some have responded well and others have not. For this reason, a sentiment analysis of the COVID-19 vaccine will be carried out by taking data from Twitter, then classified using the Support Vector Machine algorithm. The research data is nonlinear data so it requires a kernel space for the text mining process, while there has been no specific research regarding which kernel is good for sentiment analysis, so a test will be carried out to find the best kernel among linear, sigmoid, polynomial, and RBF kernels. The result is that sigmoid and linear kernels have a better value, namely 0.87 compared to RBF and polynomial, namely 0.86

EZIOTracer

Tracing is a popular method for evaluating, investigating, and modeling the performance of today's storage systems. Tracing has become crucial with the increase in complexity of modern storage applications/systems, that are manipulating an ever-increasing amount of data and are subject to extreme performance requirements. There exists many tracing tools focusing either on the user-level or the kernel-level, however we observe the lack of a unified tracer targeting both levels: this prevents a comprehensive understanding of modern applications' storage performance profiles. In this paper, we present EZIOTracer, a unified I/O tracer for both (Linux) kernel and user spaces, targeting data intensive applications. EZIOTracer is composed of a userland as well as a kernel space tracer, complemented with a trace analysis framework able to merge the output of the two tracers, and in particular to relate user-level events to kernel-level ones, and vice-versa. On the kernel side, EZIOTracer relies on eBPF to offer safe, low-overhead, low memory footprint, and flexible tracing capabilities. We demonstrate using FIO benchmark the ability of EZIOTracer to track down I/O performance issues by relating events recorded at both the kernel and user levels. We show that this can be achieved with a relatively low overhead that ranges from 2% to 26% depending on the I/O intensity.

Symmetry Based Material Optimization

Many man-made or natural objects are composed of symmetric parts and possess symmetric physical behavior. Although its shape can exactly follow a symmetry in the designing or modeling stage, its discretized mesh in the analysis stage may be asymmetric because generating a mesh exactly following the symmetry is usually costly. As a consequence, the expected symmetric physical behavior may not be faithfully reproduced due to the asymmetry of the mesh. To solve this problem, we propose to optimize the material parameters of the mesh for static and kinematic symmetry behavior. Specifically, under the situation of static equilibrium, Young’s modulus is properly scaled so that a symmetric force field leads to symmetric displacement. For kinematics, the mass is optimized to reproduce symmetric acceleration under a symmetric force field. To efficiently measure the deviation from symmetry, we formulate a linear operator whose kernel contains all the symmetric vector fields, which helps to characterize the asymmetry error via a simple ℓ2 norm. To make the resulting material suitable for the general situation, the symmetric training force fields are derived from modal analysis in the above kernel space. Results show that our optimized material significantly reduces the asymmetric error on an asymmetric mesh in both static and dynamic simulations.

Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

In recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.