# Singular value description of a digital radiographic detector: Theory and measurements

## Abstract

The H operator represents the deterministic performance of any imaging system. For a linear, digital imaging system, this system operator can be written in terms of a matrix, H, that describes the deterministic response of the system to a set of point objects. A singular value decomposition of this matrix results in a set of orthogonal functions (singular vectors) that form the system basis. A linear combination of these vectors completely describes the transfer of objects through the linear system, where the respective singular values associated with each singular vector describe the magnitude with which that contribution to the object is transferred through the system. This paper is focused on the measurement, analysis, and interpretation of the H matrix for digital x-ray detectors. A key ingredient in the measurement of the H matrix is the detector response to a single x ray (or infinitestimal x-ray beam). The authors have developed a method to estimate the 2D detector shift-variant, asymmetric ray response function (RRF) from multiple measured line response functions (LRFs) using a modified edge technique. The RRF measurements cover a range of x-ray incident angles from 0 deg. (equivalent location at the detector center) to 30 deg. (equivalent location atmore »

- Authors:

- NIBIB/CDRH Laboratory for the Assessment of Medical Imaging Systems, US Food and Drug Administration, New Hampshire Avenue, Silver Spring, Maryland 20993 (United States)

- Publication Date:

- OSTI Identifier:
- 22095229

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Medical Physics; Journal Volume: 35; Journal Issue: 10; Other Information: (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 62 RADIOLOGY AND NUCLEAR MEDICINE; CORRELATIONS; GEOMETRY; IMAGES; MATRICES; OPTICAL SYSTEMS; PERFORMANCE; RESPONSE FUNCTIONS; X RADIATION; X-RAY DETECTION; X-RAY RADIOGRAPHY

### Citation Formats

```
Kyprianou, Iacovos S., Badano, Aldo, Gallas, Brandon D., and Myers, Kyle J.
```*Singular value description of a digital radiographic detector: Theory and measurements*. United States: N. p., 2008.
Web. doi:10.1118/1.2975222.

```
Kyprianou, Iacovos S., Badano, Aldo, Gallas, Brandon D., & Myers, Kyle J.
```*Singular value description of a digital radiographic detector: Theory and measurements*. United States. doi:10.1118/1.2975222.

```
Kyprianou, Iacovos S., Badano, Aldo, Gallas, Brandon D., and Myers, Kyle J. Wed .
"Singular value description of a digital radiographic detector: Theory and measurements". United States. doi:10.1118/1.2975222.
```

```
@article{osti_22095229,
```

title = {Singular value description of a digital radiographic detector: Theory and measurements},

author = {Kyprianou, Iacovos S. and Badano, Aldo and Gallas, Brandon D. and Myers, Kyle J.},

abstractNote = {The H operator represents the deterministic performance of any imaging system. For a linear, digital imaging system, this system operator can be written in terms of a matrix, H, that describes the deterministic response of the system to a set of point objects. A singular value decomposition of this matrix results in a set of orthogonal functions (singular vectors) that form the system basis. A linear combination of these vectors completely describes the transfer of objects through the linear system, where the respective singular values associated with each singular vector describe the magnitude with which that contribution to the object is transferred through the system. This paper is focused on the measurement, analysis, and interpretation of the H matrix for digital x-ray detectors. A key ingredient in the measurement of the H matrix is the detector response to a single x ray (or infinitestimal x-ray beam). The authors have developed a method to estimate the 2D detector shift-variant, asymmetric ray response function (RRF) from multiple measured line response functions (LRFs) using a modified edge technique. The RRF measurements cover a range of x-ray incident angles from 0 deg. (equivalent location at the detector center) to 30 deg. (equivalent location at the detector edge) for a standard radiographic or cone-beam CT geometric setup. To demonstrate the method, three beam qualities were tested using the inherent, Lu/Er, and Yb beam filtration. The authors show that measures using the LRF, derived from an edge measurement, underestimate the system's performance when compared with the H matrix derived using the RRF. Furthermore, the authors show that edge measurements must be performed at multiple directions in order to capture rotational asymmetries of the RRF. The authors interpret the results of the H matrix SVD and provide correlations with the familiar MTF methodology. Discussion is made about the benefits of the H matrix technique with regards to signal detection theory, and the characterization of shift-variant imaging systems.},

doi = {10.1118/1.2975222},

journal = {Medical Physics},

number = 10,

volume = 35,

place = {United States},

year = {Wed Oct 15 00:00:00 EDT 2008},

month = {Wed Oct 15 00:00:00 EDT 2008}

}