A more accurate reconstruction system matrix for quantitative proton computed tomography

Abstract

An accurate system matrix is required for quantitative proton CT (pCT) image reconstruction with iterative projection algorithms. The system matrix is composed of chord lengths of individual proton path intersections with reconstruction pixels. In previous work, reconstructions were performed assuming constant intersection chord lengths, which led to systematic errors of the reconstructed proton stopping powers. The purpose of the present work was to introduce a computationally efficient variable intersection chord length in order to improve the accuracy of the system matrix. An analytical expression that takes into account the discrete stepping nature of the pCT most likely path (MLP) reconstruction procedure was created to describe an angle-dependent effective mean chord length function. A pCT dataset was simulated with GEANT4 using a parallel beam of 200 MeV protons intersecting a computerized head phantom consisting of tissue-equivalent materials with known relative stopping power. The phantom stopping powers were reconstructed with the constant chord length, exact chord length, and effective mean chord length approaches, in combination with the algebraic reconstruction technique. Relative stopping power errors were calculated for each anatomical phantom region and compared for the various methods. It was found that the error of approximately 10% in the mean reconstructed stopping power value for a given anatomical region, resulting from a system matrix with a constant chord length, could be reduced to less than 0.5% with either the effective mean chord length or exact chord length approaches. Reconstructions with the effective mean chord length were found to be approximately 20% faster than reconstructions with an exact chord length. The effective mean chord length method provides the possibility for more accurate, computationally efficient quantitative pCT reconstructions.

Reconstructing highly accurate relative stopping powers in proton computed tomography

“…The coordinates where these intersections occurred were recorded and then used to calculate the proton's most-likely path (MLP) through the object [8]. The MLP of protons passing through the object were then used to construct the A matrix as shown in previous studies [3], [4]. Since each proton passes through only a small portion of the reconstruction volume, the resulting A matrix is sparse and to reduce memory usage, only its nonzero elements were stored.…”

“…In this system of equations, the system matrix A describes the mean effective path length of the ith proton through the jth object voxel [3], x is the object RSP vector, and b is the vector of measured WEPL values. In previous work, the initially reconstructed FBP image was thresholded to define the object hull, while more recently we have employed hull detection techniques based on individual WEPL thresholding and space carving for better hull definition [4].…”

Characteristics of proton CT images reconstructed with filtered backprojection and iterative projection algorithms

“…The block-iterative diagonally relaxed orthogonal projections (DROP) [9] scheme was used in the current work, as promising results had been found in our previous work [14]. A recently developed method that takes variations in the voxel-intersection length into account [15] was used for the calculation of system matrix elements.…”

A Fast Experimental Scanner for Proton CT: Technical Performance and First Experience With Phantom Scans

“…The Feldkamp-Davis-Kress (FDK) algorithm [21], the cone-beam version of the FBP, is used both for boundary detection and as a starting point for the ensuing iterative reconstruction, which employs a method based on diagonally relaxed orthogonal projections (DROP) onto convex sets. This method requires knowledge of each proton’s WEPL and its MLP [22] through the phantom. It forms a large linear system of sparse equations, which is then solved iteratively for the unknown RSP object vector.…”