Singular value decomposition of pinhole SPECT systems

Robin Palit; Matthew A. Kupinski; Harrison H. Barrett; Eric W. Clarkson; John N. Aarsvold; Lana Volokh; Yariv Grobshtein

doi:10.1117/12.813799

12 March 2009 Singular value decomposition of pinhole SPECT systems

Robin Palit, Matthew A. Kupinski, Harrison H. Barrett, Eric W. Clarkson, John N. Aarsvold, Lana Volokh, Yariv Grobshtein

Author Affiliations +

Proceedings Volume 7263, Medical Imaging 2009: Image Perception, Observer Performance, and Technology Assessment; 72631U (2009) https://doi.org/10.1117/12.813799
Event: SPIE Medical Imaging, 2009, Lake Buena Vista (Orlando Area), Florida, United States

Abstract

A single photon emission computed tomography (SPECT) imaging system can be modeled by a linear operator H that maps from object space to detector pixels in image space. The singular vectors and singular-value spectra of H provide useful tools for assessing system performance. The number of voxels used to discretize object space and the number of collection angles and pixels used to measure image space make the matrix dimensions H large. As a result, H must be stored sparsely which renders several conventional singular value decomposition (SVD) methods impractical. We used an iterative power methods SVD algorithm (Lanczos) designed to operate on very large sparsely stored matrices to calculate the singular vectors and singular-value spectra for two small animal pinhole SPECT imaging systems: FastSPECT II and M³R. The FastSPECT II system consisted of two rings of eight scintillation cameras each. The resulting dimensions of H were 68921 voxels by 97344 detector pixels. The M³R system is a four camera system that was reconfigured to measure image space using a single scintillation camera. The resulting dimensions of H were 50864 voxels by 6241 detector pixels. In this paper we present results of the SVD of each system and discuss calculation of the measurement and null space for each system.

Citation Download Citation

Robin Palit, Matthew A. Kupinski, Harrison H. Barrett, Eric W. Clarkson, John N. Aarsvold, Lana Volokh, and Yariv Grobshtein "Singular value decomposition of pinhole SPECT systems", Proc. SPIE 7263, Medical Imaging 2009: Image Perception, Observer Performance, and Technology Assessment, 72631U (12 March 2009); https://doi.org/10.1117/12.813799

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