### 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.

Original language | English (US) |
---|---|

Title of host publication | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |

Volume | 7263 |

DOIs | |

State | Published - 2009 |

Event | Medical Imaging 2009: Image Perception, Observer Performance, and Technology Assessment - Lake Buena Vista, FL, United States Duration: Feb 11 2009 → Feb 12 2009 |

### Other

Other | Medical Imaging 2009: Image Perception, Observer Performance, and Technology Assessment |
---|---|

Country | United States |

City | Lake Buena Vista, FL |

Period | 2/11/09 → 2/12/09 |

### Fingerprint

### Keywords

- Lanczos
- Singular value decomposition
- Sparse matrix
- SPECT

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Electronic, Optical and Magnetic Materials
- Biomaterials
- Radiology Nuclear Medicine and imaging

### Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(Vol. 7263). [72631U] https://doi.org/10.1117/12.813799

**Singular value decomposition of pinhole SPECT systems.** / Palit, Robin; Kupinski, Matthew A; Barrett, Harrison H; Clarkson, Eric W; Aarsvold, John N.; Volokh, Lana; Grobshtein, Yariv.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE.*vol. 7263, 72631U, Medical Imaging 2009: Image Perception, Observer Performance, and Technology Assessment, Lake Buena Vista, FL, United States, 2/11/09. https://doi.org/10.1117/12.813799

}

TY - GEN

T1 - Singular value decomposition of pinhole SPECT systems

AU - Palit, Robin

AU - Kupinski, Matthew A

AU - Barrett, Harrison H

AU - Clarkson, Eric W

AU - Aarsvold, John N.

AU - Volokh, Lana

AU - Grobshtein, Yariv

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Lanczos

KW - Singular value decomposition

KW - Sparse matrix

KW - SPECT

UR - http://www.scopus.com/inward/record.url?scp=67249091485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67249091485&partnerID=8YFLogxK

U2 - 10.1117/12.813799

DO - 10.1117/12.813799

M3 - Conference contribution

SN - 9780819475145

VL - 7263

BT - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

ER -