## Abstract

This chapter discusses how 2‑D or 3‑D images of tracer distribution can be reconstructed from a series of so-called projection images acquired with a gamma camera or a positron emission tomography (PET) system [13.1]. This is often called an ‘inverse problem’. The reconstruction is the inverse of the acquisition. The reconstruction is called an inverse problem because making software to compute the true tracer distribution from the acquired data turns out to be more difficult than the ‘forward’ direction, i.e. making software to simulate the acquisition. There are basically two approaches to image reconstruction: analytical reconstruction and iterative reconstruction. The analytical approach is based on mathematical inversion, yielding efficient, non-iterative reconstruction algorithms. In the iterative approach, the reconstruction problem is reduced to computing a finite number of image values from a finite number of measurements. That simplification enables the use of iterative instead of mathematical inversion. Iterative inversion tends to require more computer power, but it can cope with more complex (and hopefully more accurate) models of the acquisition process.

Nuyts, J.;

^{[1] }Matej, S.^{[2] }- Department of Nuclear Medicine and Medical Imaging Research Center, Katholieke Universiteit Leuven, Leuven (Belgium)
- Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, PA (United States)

## Citation Formats

Nuyts, J., and Matej, S.
Image Reconstruction. Chapter 13.
IAEA: N. p.,
2014.
Web.

Nuyts, J., & Matej, S.
Image Reconstruction. Chapter 13.
IAEA.

Nuyts, J., and Matej, S.
2014.
"Image Reconstruction. Chapter 13."
IAEA.

@misc{etde_22327864,

title = {Image Reconstruction. Chapter 13}

author = {Nuyts, J., and Matej, S.}

abstractNote = {This chapter discusses how 2‑D or 3‑D images of tracer distribution can be reconstructed from a series of so-called projection images acquired with a gamma camera or a positron emission tomography (PET) system [13.1]. This is often called an ‘inverse problem’. The reconstruction is the inverse of the acquisition. The reconstruction is called an inverse problem because making software to compute the true tracer distribution from the acquired data turns out to be more difficult than the ‘forward’ direction, i.e. making software to simulate the acquisition. There are basically two approaches to image reconstruction: analytical reconstruction and iterative reconstruction. The analytical approach is based on mathematical inversion, yielding efficient, non-iterative reconstruction algorithms. In the iterative approach, the reconstruction problem is reduced to computing a finite number of image values from a finite number of measurements. That simplification enables the use of iterative instead of mathematical inversion. Iterative inversion tends to require more computer power, but it can cope with more complex (and hopefully more accurate) models of the acquisition process.}

place = {IAEA}

year = {2014}

month = {Dec}

}

title = {Image Reconstruction. Chapter 13}

author = {Nuyts, J., and Matej, S.}

abstractNote = {This chapter discusses how 2‑D or 3‑D images of tracer distribution can be reconstructed from a series of so-called projection images acquired with a gamma camera or a positron emission tomography (PET) system [13.1]. This is often called an ‘inverse problem’. The reconstruction is the inverse of the acquisition. The reconstruction is called an inverse problem because making software to compute the true tracer distribution from the acquired data turns out to be more difficult than the ‘forward’ direction, i.e. making software to simulate the acquisition. There are basically two approaches to image reconstruction: analytical reconstruction and iterative reconstruction. The analytical approach is based on mathematical inversion, yielding efficient, non-iterative reconstruction algorithms. In the iterative approach, the reconstruction problem is reduced to computing a finite number of image values from a finite number of measurements. That simplification enables the use of iterative instead of mathematical inversion. Iterative inversion tends to require more computer power, but it can cope with more complex (and hopefully more accurate) models of the acquisition process.}

place = {IAEA}

year = {2014}

month = {Dec}

}