Expectation Maximization iterative reconstruction algorithms are being widely used in PET and SPECT imaging. The system probability matrix is usually calculated by using Monte Carlo simulations, since the analytical calculation is a rather complicated problem, especially in 3D reconstruction; however, realistic Monte Carlo simulations in 3D are time consuming and simplifications are necessary. ...

Monte Carlo simulations are nowadays an essential tool in emission tomography (Single-Photon Emission Computed Tomography— SPECT and Positron Emission Tomography—PET), for assisting system design and optimizing imaging and processing protocols. Several Monte Carlo simulation software are currently available for modeling SPECT and PET configurations. This paper presents an overview of current tr...

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo (i.e. diffusion Monte Carlo wit...

Volume measurement plays an important role in the production and processing of food products. Various methods have been proposed to measure the volume of food products with irregular shapes based on 3D reconstruction. However, 3D reconstruction comes with a high-priced computational cost. Furthermore, some of the volume measurement methods based on 3D reconstruction have a low accuracy. Another...

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does...

The problem of global illumination in computer graphics is described by a Fredholm integral equation of the second kind. Due to the complexity of this equation, Monte Carlo methods provide an efficient tool for the estimation of the solution. A new approach, using quasi-Monte Carlo integration, is introduced and compared to Monte Carlo integration. We discuss some theoretical aspects and give n...