User's guide to SFTRAN/1100

Extensions and improvements were made to SFTRAN, a structured programming language. This language was implemented as a precompiler that translates from SFTRAN to FORTRAN. It was available to batch and conversational users of the UNIVAC 1100 computer system. The SFTRAN language and its use are described. In addition, conversational time-sharing system command subroutines were implemented that eliminated the complications of dealing with extra files and processing steps that the use of a precompiler would otherwise require. These command subroutines are reported, and their use is illustrated by examples

User's guide for SFTRAN/360

Extension and improvements made to SFTRAN, a structured-programming language are discussed. This improved language is implemented as a precompiler that translates from SFTRAN to FORTRAN. The SFTRAN language and its use are described. Time-Sharing System (TSS) command procedures were implemented that eliminate the complications of dealing with extra files and processing steps which the use of a precompiler would otherwise require. These command procedures are described and their use is illustrated by examples

Mean and Variance of Photon Counting with Deadtime

The statistics of photon counting by systems affected by deadtime are potentially important for statistical image reconstruction methods. We present a new way of analyzing the moments of the counting process for a counter system affected by various models of deadtime related to PET and SPECT imaging. We derive simple and exact expressions for the first and second moments of the number of recorded events under various models. From our mean expression for a SPECT deadtime model, we derive a simple estimator for the actual intensity of the underlying Poisson process; simulations show that our estimator is unbiased even for extremely high count rates.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85820/1/Fessler158.pd

Edge-Preserving Tomographic Reconstruction with Nonlocal Regularization

Tomographic image reconstruction using statistical methods can provide more accurate system modeling, statistical models, and physical constraints than the conventional filtered backprojection (FBP) method. Because of the ill posedness of the reconstruction problem, a roughness penalty is often imposed on the solution to control noise. To avoid smoothing of edges, which are important image attributes, various edge-preserving regularization methods have been proposed. Most of these schemes rely on information from local neighborhoods to determine the presence of edges. In this paper, we propose a cost function that incorporates nonlocal boundary information into the regularization method. We use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function, jointly estimating region boundaries and object pixel values. We apply variational techniques implemented using level-sets methods to update the boundary estimates; then, using the most recent boundary estimate, we minimize a space-variant quadratic cost function to update the image estimate. For the positron emission tomography transmission reconstruction application, we compare the bias-variance tradeoff of this method with that of a "conventional" penalized-likelihood algorithm with local Huber roughness penalty.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85989/1/Fessler73.pd

Maximum-Likelihood Transmission Image Reconstruction for Overlapping Transmission Beams

In many transmission imaging geometries, the transmitted "beams" of photons overlap on the detector, such that a detector element may record photons that originated in different sources or source locations and thus traversed different paths through the object. Examples include systems based on scanning line sources or on multiple parallel rod sources. The overlap of these beams has been disregarded by both conventional analytical reconstruction methods as well as by previous statistical reconstruction methods. The authors propose a new algorithm for statistical image reconstruction of attenuation maps that explicitly accounts for overlapping beams in transmission scans. The algorithm is guaranteed to monotonically increase the objective function at each iteration. The availability of this algorithm enables the possibility of deliberately increasing the beam overlap so as to increase count rates. Simulated single photon emission tomography transmission scans based on a multiple line source array demonstrate that the proposed method yields improved resolution/noise tradeoffs relative to "conventional" reconstruction algorithms, both statistical and nonstatistical.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85818/1/Fessler78.pd

Maximum Likelihood Transmission Image Reconstruction for Over lapping Transmission Beams

In many transmission imaging geometries, the transmitted “beams” of photons overlap on the detector, such that a detector element may record photons that originated in different sources or source locations and thus traversed different paths through the object, Examples include systems based on scanning line sources or on multiple parallel rod sources. The overlap of these beams has been disregarded by both conventional analytical reconstruction methods as well as by previous statistical reconstruction methods. We propose a new algorithm for statistical image reconstruction of attenuation maps that explicitly accounts for overlapping beams in transmission scans. The algorithm is guaranteed to monotonically increase the objective function at each iteration. The availability of this algorithm enables the possibility of deliberately increasing the beam overlap so as to increase count rates. Simulated SPECT transmission scans based on a multiple line source array demonstrate that the proposed method yields improved resolution/noise tradeoffs relative to “conventional” reconstruction algorithms, both statistical and nonstatistical.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85817/1/Fessler156.pd

Quantitative I-131 SPECT Reconstruction using CT Side Information from Hybrid Imaging

A penalized-likelihood (PL) SPECT reconstruction method using a modified regularizer that accounts for anatomical boundary side information was implemented to achieve accurate estimates of both the total target activity and the activity distribution within targets. In both simulations and experimental I-131 phantom studies, reconstructions from 1) penalized likelihood employing CT-side information based regularization (PL-CT); 2) penalized likelihood with edge preserving regularization (no CT); 3) penalized likelihood with conventional spatially invariant quadratic regularization (no CT) were compared with 4) Ordered Subset Expectation Maximization (OSEM), which is the iterative algorithm conventionally used in clinics for quantitative SPECT. Evaluations included phantom studies with perfect and imperfect (misregistered) side information and studies with uniform and non-uniform activity distributions in the target. For targets with uniform activity, the PL-CT images and profiles were closest to the `truth', avoided the edge offshoots evident with OSEM and minimized the blurring across boundaries evident with regularization without CT information. Apart from visual comparison, reconstruction accuracy was evaluated using the bias and standard deviation (STD) of the total target activity estimate and the root mean square error (RMSE) of the activity distribution within the target. PL-CT reconstruction reduced both bias and RMSE compared with regularization without side information. When compared with unregularized OSEM, PL-CT reduced RMSE and STD while bias was comparable. For targets with non-uniform activity, these improvements with PL-CT were observed only when the change in activity was matched by a change in the anatomical image and the corresponding inner boundary was also used to control the regularization. In summary, the present work demonstrates the potential of using CT side information to obtain improved estimates of the activity distribution in targets wi- - thout sacrificing the accuracy of total target activity estimation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85862/1/Fessler243.pd

Regularized reconstruction in quantitative SPECT using CT side information from hybrid imaging

A penalized-likelihood (PL) SPECT reconstruction method using a modified regularizer that accounts for anatomical boundary side information was implemented to achieve accurate estimates of both the total target activity and the activity distribution within targets. In both simulations and experimental I-131 phantom studies, reconstructions from (1) penalized likelihood employing CT-side information-based regularization (PL-CT), (2) penalized likelihood with edge preserving regularization (no CT) and (3) penalized likelihood with conventional spatially invariant quadratic regularization (no CT) were compared with (4) ordered subset expectation maximization (OSEM), which is the iterative algorithm conventionally used in clinics for quantitative SPECT. Evaluations included phantom studies with perfect and imperfect side information and studies with uniform and non-uniform activity distributions in the target. For targets with uniform activity, the PL-CT images and profiles were closest to the 'truth', avoided the edge offshoots evident with OSEM and minimized the blurring across boundaries evident with regularization without CT information. Apart from visual comparison, reconstruction accuracy was evaluated using the bias and standard deviation (STD) of the total target activity estimate and the root mean square error (RMSE) of the activity distribution within the target. PL-CT reconstruction reduced both bias and RMSE compared with regularization without side information. When compared with unregularized OSEM, PL-CT reduced RMSE and STD while bias was comparable. For targets with non-uniform activity, these improvements with PL-CT were observed only when the change in activity was matched by a change in the anatomical image and the corresponding inner boundary was also used to control the regularization. In summary, the present work demonstrates the potential of using CT side information to obtain improved estimates of the activity distribution in targets without sacrificing the accuracy of total target activity estimation. The method is best suited for data acquired on hybrid systems where SPECT-CT misregistration is minimized. To demonstrate clinical application, the PL reconstruction with CT-based regularization was applied to data from a patient who underwent SPECT/CT imaging for tumor dosimetry following I-131 radioimmunotherapy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85409/1/pmb10_9_007.pd