System Matrix Analysis for Computed Tomography Imaging

Abstract

In practical applications of computed tomography imaging (CT), it is often the case that the set of projection data is incomplete owing to the physical conditions of the data acquisition process. On the other hand, the high radiation dose imposed on patients is also undesired. These issues demand that high quality CT images can be reconstructed from limited projection data. For this reason, iterative methods of image reconstruction have become a topic of increased research interest. Several algorithms have been proposed for few-view CT. We consider that the accurate solution of the reconstruction problem also depends on the system matrix that simulates the scanning process. In this work, we analyze the application of the Siddon method to generate elements of the matrix and we present results based on real projection data.

QR-Factorization Algorithm for Computed Tomography (CT): Comparison With FDK and Conjugate Gradient (CG) Algorithms

“…The system matrix that describes the scanning process has a major impact on the quality of the reconstructed image [34]. There are two main points to take into account for designing the system matrix:…”

An FPGA-based analysis of trade-offs in the presence of ill-conditioning and different precision levels in computations

“…In the former case, the Tikhonov filter uses a temporal data deconvolution method in the filtered back-projection algorithm [13]. In the latter, due to the physical conditions of the data acquisition process, it is common to find a noisy, incomplete set of unequally spaced projections wherein this problem is ill-posed [14]. One more application in which matrices are used consists of Polynomial probability distribution estimation based on N statistical moments from each distribution, which is essential in applied statistical analysis in diverse scientific fields [15].…”