Selection of the most sensitive configuration of strip array detectors for x-ray beam monitoring in radiotherapy of cancer utilizing singular value decomposition

Abstract

We propose a concise mathematical framework in order to compare detector configurations efficiently for x-ray beam monitoring in radiotherapy of cancer. This framework consists of the singular value decomposition (SVD) of the system matrix and the definition of an effective information threshold based on the relative error inequality utilizing the condition number of a matrix. The goal of this paper is to present the mathematical argument as well as to demonstrate its use for modeling the best detector configuration for monitoring x-ray beams in external beam therapy. This analysis depends neither on specific measurements of a given set of x-ray beams, nor does it depend in specific reconstruction algorithms of the beam shape, and therefore represents a configuration meta-analysis. In the results section, we compare three possible detector designs, each leading to a highly underdetermined system, and are able to determine their effective information content relative to each other. Furthermore, by changing design parameters, such as the geometric detector configuration, number of detectors, detector pixel size, and the x-ray beam blur, deeper insight in this challenging inverse problem is achieved and the most sensitive monitoring scheme is determined.Graphical Illustration of the general approach for performing configuration meta–analysis.