Two popular model reduction methods, the proper orthogonal decomposition (POD), and balanced truncation, are applied together with Galerkin projection to the twodimensional Burgers’ equation. This scalar equation is chosen because it has a nonlinearity that is similar to the NavierStokes equation, but it can be accurately simulated using far fewer states. However, the number of states required ...

Recently, a novel method for region of interest (ROI) reconstruction from truncated projections with neither the use of prior knowledge nor explicit extrapolation has been published, named Approximated Truncation Robust Algorithm for Computed Tomography (ATRACT). It was derived by analytically reformulating the standard Feldkamp-Davis-Kress (FDK) algorithm into a reconstruction scheme that is b...

An orbit geometry where the central projection ray of the detector is not constrained to pass through the center-of-rotation for all projection angles can be useful to reduce uniformity artifacts and to avoid truncation when imaging non centrally located organs. We present a backprojection filtering algorithm for parallel geometry with an elliptical orbit acquisition and verify the algorithm by...

The paper presents a novel approach for a balanced truncation style of model reduction of a perturbative representation of a nonlinear system. Empirical controllability and observability gramians for nonlinear systems are employed to define a projection matrix. However, the projection matrix is applied to the perturbative representation of the system rather than directly to the exact nonlinear ...

Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture dynamics. For nonlinear operating far away from equilibria, on other hand, current approaches seek low-dimensional representations state often neglect low-energy features have high significance. ...

INTRODUCTION Designing control system by using the H∞ or μ -synthesis leads to a high-order controller due to using the frequency weighting filter to envelop the uncertainty factors. In most practical circumstances, it is desirable to reduce the controller order. Moreover, any controller order reduction method should take into account closed-loop stability and other specific performance aspects...

UNLABELLED We studied the bias and variance characteristics of the ordered-subset expectation maximization (OSEM) and rescaled block-iterative EM (RBIEM) iterative reconstruction algorithms in myocardial SPECT under extreme, but realistic, conditions. METHOD We used the 2-dimensional mathematic cardiac torso phantom to simulate 2 patient anatomies: a large male with a raised diaphragm and a f...

Reduced-order models for plane Couette flow are obtained by Galerkin projection of the Navier-Stokes equations onto leading controllability modes linearized system. Nonlinear dynamical systems so constructed, with various degrees truncation, numerically stable and reproduce statistics minimal turbulent at Reynolds numbers 500 1200 different choices modal bases. A closure model was not included ...

Background: The limited transaxial field-of-view (FOV) of a very small cardiac SPECT camera system causes view-dependent truncation of the projection of structures exterior to, but near the heart. Basic tomographic principles suggest that the reconstruction of non-attenuated truncated data gives a distortion-free image in the interior of the truncated region, but the DC term of the Fourier spec...