Approximate 3D iterative reconstruction for SPECT

Abstract

Compared with slice-by-slice approaches for SPECT reconstruction, three-dimensional iterative methods provide a more accurate physical model and an improved SPECT image. Clinical application of these methods, however, is limited primarily to their computational demands. This paper investigates the methods for approximate 3D iterative reconstruction that greatly reduce this demand by excluding from the reconstruction the smaller magnitude elements of the system matrix. A new method is described which is designed to control the resulting bias in the SPECT image for a given reduction in computation. The approximate methods were compared to fully 3D iterative reconstruction in terms of SPECT image bias and visual quality. All methods were incorporated into the ML-EM algorithm and applied to data from 3D mathematical and experimental brain phantoms. The SPECT images reconstructed by the approximate methods exhibited a positive bias throughout the image that was in general smaller with the new method (in the rage of 2%-6%). The bias was smallest in locally hot regions and largest in locally cold regions. The high quality brain phantom images demonstrated the capability of the new method in realistic imaging contexts. The time per iteration for an entire 3D brain phantom on a modern workstation using the approximate 3D method was 7.0 s.

A residual correction method for high‐resolution PET reconstruction with application to on‐the‐fly Monte Carlo based model of positron range

“…[35][36][37] However, there exists a wide variety of alternatives to construct the approximate system matrix being used in the proposed method. For example, an approximate system matrix may be obtained by reducing the number of nonzero elements to make it more sparse, 7,45 or using fast forward and back projectors based on Fourier slice theorem 46 and Fourier rebinning. 47 The proposed method may also be used in combination with image reconstruction algorithms running on modern vector computing platforms such as graphical processing units, 48 where the simplified system model can be tailored to take advantage of special features of the hardware.…”

A slice-by-slice blurring model and kernel evaluation using the Klein-Nishina formula for 3D scatter compensation in parallel and converging beam SPECT

“…Another class of scatter compensation methods is based on modelling scatter effects (the scatter response function) in the projector-backprojector (transition matrix) used in iterative reconstruction methods (Floyd et al 1985b, Frey et al 1993, Frey and Tsui 1993, Beekman et al 1993, 1996, Welch et al 1995. The techniques for modelling the non-uniform attenuation effect (Tsui et al 1989), the detector response effect (Tsui et al 1988, 1994, Formiconi et al 1989, Zeng et al 1991, Gilland et al 1994 and the scatter effect (Floyd et al 1985b, 1986, Veklerov et al 1988, Frey and Tsui 1990, 1994, 1996, Bowsher and Floyd 1991, Frey et al 1992, Beekman et al 1993, 1994, 1996, 1997, Riauka and Gortel 1994, Cao et al 1994, Meikle et al 1994, Walrand et al 1994, Ju et al 1995, Welch et al 1995, Kadrmas et al 1996, 1997, Hutton et al 1996, Riauka et al 1996, Wells et al 1997, Hutton 1997) in a realistic projector-backprojector (transition matrix) may lead to accurate compensation for these image-degrading effects in SPECT image reconstruction. We call this class of methods reconstruction-based scatter compensation methods.…”