### Abstract

Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

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

Pages (from-to) | 7359-7385 |

Number of pages | 27 |

Journal | Physics in Medicine and Biology |

Volume | 60 |

Issue number | 18 |

DOIs | |

State | Published - Sep 21 2015 |

### Fingerprint

### Keywords

- analytic reconstruction
- LM acquisition
- null functions
- photon-processing systems
- singular-value decomposition
- SPECT

### ASJC Scopus subject areas

- Radiology Nuclear Medicine and imaging
- Radiological and Ultrasound Technology

### Cite this

*Physics in Medicine and Biology*,

*60*(18), 7359-7385. https://doi.org/10.1088/0031-9155/60/18/7359

**Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions.** / Jha, Abhinav K.; Barrett, Harrison H; Frey, Eric C.; Clarkson, Eric W; Caucci, Luca; Kupinski, Matthew A.

Research output: Contribution to journal › Article

*Physics in Medicine and Biology*, vol. 60, no. 18, pp. 7359-7385. https://doi.org/10.1088/0031-9155/60/18/7359

}

TY - JOUR

T1 - Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions

AU - Jha, Abhinav K.

AU - Barrett, Harrison H

AU - Frey, Eric C.

AU - Clarkson, Eric W

AU - Caucci, Luca

AU - Kupinski, Matthew A

PY - 2015/9/21

Y1 - 2015/9/21

N2 - Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

AB - Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

KW - analytic reconstruction

KW - LM acquisition

KW - null functions

KW - photon-processing systems

KW - singular-value decomposition

KW - SPECT

UR - http://www.scopus.com/inward/record.url?scp=84941083342&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941083342&partnerID=8YFLogxK

U2 - 10.1088/0031-9155/60/18/7359

DO - 10.1088/0031-9155/60/18/7359

M3 - Article

C2 - 26350439

AN - SCOPUS:84941083342

VL - 60

SP - 7359

EP - 7385

JO - Physics in Medicine and Biology

JF - Physics in Medicine and Biology

SN - 0031-9155

IS - 18

ER -