Accurate and robust tomographic reconstruction from dynamic positron emission tomography (PET) acquired data is a difficult problem. Conventional methods, such as the maximum likelihood expectation maximization (MLEM) algorithm for reconstructing the activity distribution-based on individual frames, may lead to inaccurate results due to the checkerboard effect and limitation of photon counts. I...

In this paper, we (re)introduce the independent gamma prior for penalized likelihood reconstruction for both emission and transmission tomography. We give the expressions for bias and variance, and validate the expressions using Monte Carlo simulations. We also test a plug-in approach to get an approximate estimate of the variance image. We list the fixed point local point-spread function expre...

We propose a bilinear sampling algorithm in Green’s function Monte Carlo for expectation values of operators that do not commute with the Hamiltonian and for differences between eigenvalues of different Hamiltonians. The integral representations of the Schroedinger equations are transformed into two equations whose solution has the form ψa(x)t(x, y)ψb(y), where ψa and ψb are the wavefunctions f...

The path integral Monte Carlo calculated radial distributions of para-hydrogen clusters (p-H2)N consisting of N = 4−40 molecules interacting via a Lennard-Jones potential at T = 1.5 K show evidence for additional peaks compared to radial distributions calculated by diffusion Monte Carlo (T = 0 K) and path integral Monte Carlo at T ≤ 0.5 K. The difference in structures is attributed to quantum d...

Electrical Capacitance Tomography is an ill-posed inverse problem that aims at recovering the spatial permittivity distribution of an inhomogeneous medium from capacitance measurements at the boundary. We consider the problem of fast robust estimation of inclusion shape and position in binary mixtures. The boundary of the inclusion is represented implicitly using a radial basis function represe...

The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sd-pf shell nuclei, a discussion of electron-capture rates in pf -shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare...

This tutorial describes numerical methods that are known as Monte Carlo methods. It starts with a basic description of the principles of Monte Carlo methods. It then discusses four individual Monte Carlo methods, describing each individual method and illustrating their use in calculating an integral. These four methods have been implemented in my example program 8.2, and the results from these ...

Developing image reconstruction algorithms for diagnostic medical devices requires physically accurate and effective simulation tools. In this paper we present a hybrid Monte Carlo (MC) particle simulation method for Computed Tomography (CT) scanners. To meet the performance requirements, we combine several variance reduction techniques and tailor the algorithms for effective GPU execution. Var...

For Halloween, we come as a math course 1 Monte Carlo Integration Suppose we want to evaluate a definite integral,

For Halloween, we come as a math course 1 Monte Carlo Integration Suppose we want to evaluate a definite integral,