In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition algorithm theoretically yields a converged transformation that balances the Gramians (including the unstable subspace). We then apply the method to a spatially d...

This paper presents an extended three-dimensional (3D) exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is t...

In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at eve...

A small detector or limited gantry rotation angles may cause data truncation, in which case the entire object cannot be completely reconstructed. However, a small region of interest (ROI) may be recoverable in certain truncation situations. Two analytical methods have been proposed for exact ROI reconstruction. Here we evaluate the capability of ROI reconstruction using an maximum-likelihood ex...

We consider the interpolation problem associated with back-projection (BP), fast BP (FBP), and factorized (FFBP) algorithms exploited in synthetic aperture radar (SAR). The 2-D required by FBP FFBP must be properly performed to mitigate effect of truncation error achieve accurate results, can effectively adopting nonuniform Fourier transform (NUFFT) routines.

We present a formal procedure for structure-preserving model reduction of linear second-order and Hamiltonian control problems that appear in a variety of physical contexts, e.g., vibromechanical systems or electrical circuit design. Typical balanced truncation methods that project onto the subspace of the largest Hankel singular values fail to preserve the problem’s physical structure and may ...

Recently, a reconstruction algorithm for region of interest (ROI) imaging in C-arm CT was published, named Approximated Truncation Robust Algorithm for Computed Tomography (ATRACT). Even in presence of severe data truncation, it is able to reconstruct images without the use of any explicit extrapolation or prior knowledge. However, this method suffers from a scaling artifact in the reconstructi...

We study theL1-stability and error estimates of general approximate solutions for the Cauchy problem associated with multidimensional Hamilton-Jacobi (H-J) equations. For strictly convex Hamiltonians, we obtain a priori error estimates in terms of the truncation errors and the initial perturbation errors. We then demonstrate this general theory for two types of approximations: approximate solut...

We introduce the exit time finite state projection (ETFSP) scheme, a truncation-based method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first passage to the complement of the domain) of a continuous-time Markov chain. We prove that: (i) the computed approximations bound the desired measures from be...