1. Introduction

Approximately 30 years have passed since Dr. Hounsfield developed a practical computed tomography (CT) system. The arrival of CT devices in the field of medical diagnosis has led to a revolution equivalent to the discovery of X-rays by Dr. Roentgen. Since then, most researchers who aim to improve medical diagnosis quality have worked toward the functional improvement of CT instruments, thus leading to the development of fan-beam CT, helical scan CT, multislice CT, and cone-beam CT instruments. These new instruments reduce the time needed for image reconstruction and significantly improve image quality. Given the increasing demand for better technology, there has been continued research and development of highperformance CT instruments.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Interest in digital tomosynthesis (DT) and its clinical applications has been revived by recent advances in digital X-ray detector technology. Conventional tomography technology provides planar information about an object from its projection images. In tomography, an X-ray tube and an X-ray film receptor lie on either side of the object. The relative motion of the tube and film is predetermined on the basis of the location of the in-focus plane [1]. A single image plane is generated by a scan, and multiple scans are required to provide a sufficient number of planes to cover the selected structure in the object. DT acquires only one set of discrete X-ray projections that can be used to reconstruct any plane of the object retrospectively [2]. The technique has been investigated in angiography and in the imaging of the chest, hand joints, lungs, teeth, and breasts [3–8]. Dobbins et al. [9] reviewed DT and showed that it outperformed planar imaging to a statistically significant extent. Various types of DT reconstruction methods have been explored.

many projections, information about the object is well sampled, and the object can be restored

In three-dimensional (3D) cone-beam imaging, information about the object in Fourier space is related to the Radon transform of the object. The relationship between the Radon transform and cone-beam projections has been well studied, and solutions to the cone-beam reconstruction have been provided [14, 15]. The Feldkamp algorithm generally provides a high degree of precision for 3D reconstruction images when an exact type of algorithm is employed [16]. Therefore, this method has been adopted for the image reconstruction of 3D tomography and multidetector cone-beam CT. A number of improved 3D reconstruction methods have been

We denoted the intensity of the incident X-rays as I<sup>0</sup> ¼ ð Þ δ; c; d and that of the X-rays that passed through the structure at the location ð Þ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup> as <sup>I</sup> <sup>¼</sup> ð Þ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup> . The image data dF <sup>¼</sup> ð Þ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup>

dFð Þ¼ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup> ln <sup>I</sup>0ð Þ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup>

R2 U2

U Xð Þ¼ ; Y; δ R þ X cos δ þ Y sin δ

c Xð Þ¼ ;Y; <sup>δ</sup> <sup>R</sup> �<sup>X</sup> sin <sup>δ</sup> <sup>þ</sup> <sup>Y</sup> cos <sup>δ</sup>

R þ X cos δ þ Y sin δ

R þ X cos δ þ Ysinδ

<sup>R</sup><sup>2</sup> <sup>þ</sup> <sup>c</sup><sup>2</sup> <sup>þ</sup> <sup>d</sup><sup>2</sup> <sup>p</sup> dFð Þ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup> !

where the projection angle <sup>δ</sup>, fan-angle <sup>γ</sup>, source trajectory <sup>R</sup>, acquisition angle <sup>θ</sup>, and gpð Þ <sup>γ</sup> represent a convolution with the Ramachandran–Lakshminarayanan filter. The Ramachandran–

ð Þ¼ <sup>γ</sup> <sup>γ</sup>

An IR algorithm performs the reconstruction in a recursive fashion [17, 18], unlike the one-step operation in backprojection and FBP algorithms. During IR, a 3D object model is repeatedly

sin α � �<sup>2</sup>

ðθ �θ

d Xð Þ¼ ;Y;Z; <sup>δ</sup> <sup>Z</sup> <sup>R</sup>

<sup>~</sup>dFð Þ¼ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup> <sup>R</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

gp

Lakshminarayanan (ramp) filter is shown below:

2.3. IR

The original projection data are used to generate an FBP image:

f FDK <sup>¼</sup> <sup>I</sup>ð Þ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup> (1)

State-Of-The-Art X-Ray Digital Tomosynthesis Imaging http://dx.doi.org/10.5772/intechopen.81667 69

<sup>~</sup>dFð Þ <sup>δ</sup>; <sup>c</sup>; <sup>d</sup> <sup>D</sup><sup>δ</sup> (2)

<sup>∗</sup>g<sup>P</sup>ð Þ <sup>γ</sup>

(3)

by combining the information from all projections.

derived from the Feldkamp algorithm.

were calculated as follows:

Current DT mainly involves image acquisition/reconstruction using polychromatic imaging. Material decomposition or virtual monochromatic image processing using dual energy (DE) has been studied in CT, and many basic and clinically useful applications have been reported [10–12]. Similar to CT, it can be expected that DT also benefits from image quality improvements. In this chapter, the fundamental image quality characteristics of various reconstruction algorithms (including a state-of-the-art reconstruction algorithm) using polychromatic imaging and virtual monochromatic DT imaging that were verified in phantom experiments are discussed.
