PURPOSE To calculate the output factor (OPF) of any irregularly shaped electron beam at extended SSD. METHODS Circular cutouts were prepared from 2.0 cm diameter to the maximum possible size for 15 × 15 applicator cone. In addition, two irregular cutouts were prepared. For each cutout, percentage depth dose (PDD) at the standard SSD and doses at different SSD values were measured using 6, 9, ...

We propose a class of quadratic optimization problems whose exact optimal objective values can be computed by their completely positive cone programming relaxations. The objective function can be any quadratic form. The constraints of each problem are described in terms of quadratic forms with no linear terms, and all constraints are homogeneous equalities, except one inhomogeneous equality whe...

A significant special case of the problems which could be solved were those whose constraints were given by semidefinite cones. A Semidefinite Program (SDP) is an optimisation over the intersection of an affine set and cone of positive semidefinite matrices (Alizadeh and Goldfarb, 2001). Cone programming is discussed more in Section 3. Within semidefinite programming there is a smaller set of p...

We propose a new fast Feldkamp algorithm for 3-D cone beam tomography with a circular source trajectory. The algorithm is an extension of our recent fast native 2-D fan-beam reconstruction algorithm. It is based on a recursive hierarchical decomposition of the cone-beam backprojection operation into successively smaller sub-volumes. The algorithm reduces the computational complexity of the reco...

This paper is concerned with so-called generic properties of general linear cone programs. Many results have been obtained on this subject during the last two decades. It has, e.g., been shown in [29] that uniqueness, strict complementarity and nondegeneracy of optimal solutions hold for almost all problem instances. Strong duality holds generically in a stronger sense: it holds for a generic s...

This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...

Several types of relaxations for binary quadratic polynomial programs can be obtained using linear, secondorder cone, or semidefinite techniques. In this paper, we propose a general framework to construct conic relaxations for binary quadratic polynomial programs based on polynomial programming. Using our framework, we re-derive previous relaxation schemes and provide new ones. In particular, w...

A new analytical method for tomographic image reconstruction from cone-beam projections acquired on the source orbits lying on a cylinder is presented. By application of a weighted cone-beam backprojection, the reconstruction problem is reduced to an image-restoration problem characterized by a shift-variant point-spread function that is given analytically. Assuming that the source is relativel...

Head motion during brain CT studies can adversely affect the reconstructed image through distortion and other artifacts such as blurring and doubling, thereby losing substantial information. In this paper, we propose a method to detect and eliminate motion artifacts in Feldkamp-David-Kress (FDK) based three-dimensional (3D) cone-beam tomography. Motion detection is achieved by comparing the cor...