^{1, 2}

^{3}

^{4}

^{5}

^{1, 2, 3}

^{1}

^{2}

^{3}

^{4}

^{5}

Current computed tomography (CT) scanners, including micro-CT scanners, utilize a point x-ray source. As we target higher and higher spatial resolutions, the reduced x-ray focal spot size limits the temporal and contrast resolutions achievable. To overcome this limitation, in this paper we propose to use a line-shaped x-ray source so that many more photons can be generated, given a data acquisition interval. In reference to the simultaneous algebraic reconstruction technique (SART) algorithm for image reconstruction from projection data generated by an x-ray point source, here we develop a generalized SART algorithm for image reconstruction from projection data generated by an x-ray line source. Our numerical simulation results demonstrate the feasibility of our novel line-source based x-ray CT approach and the proposed generalized SART algorithm.

Since the first computed tomography (CT) scanner was made [

In contrast to recently proposed source configurations, like the multiplexed [

A line-shaped x-ray source can be fabricated using field emission x-ray source technology. Field emitters have been used as electron sources for a long time. The most significant difference between the field emission x-ray tube and existing tubes lies in the field emitter cathode. The cathode can be made with an array of micromachined field emission tips. By doing so, it is possible to obtain very sharp tips and very close proximity between the tips and the gate electrode. This greatly reduces the potential difference between the tip and the gate required to achieve the field emission. The array may also be very densely packed. As a result, even though the current that can be obtained from a single tip is small, the total current that can be obtained from an array can be much larger. Schwoebel et al. [

The organization of this paper is as follows. In the next section, we formulate a forward imaging model assuming a line source. In the third section, we develop a generalized simultaneous algebraic reconstruction technique (SART) to enable line-source based reconstruction. In the fourth section, we perform numerical tests to demonstrate the performance of our technique. In the last section, we discuss relevant issues and conclude the paper.

As shown in Figure

Line x-ray source acquisition geometry.

If the length of the line is infinitesimally small, the x-ray attenuation model of a point source can be obtained by removing the outer integral in (

CT image reconstruction is a typical inverse problem of recovering

Although iterative methods have not been employed by any commercial CT scanners due to high computational costs associated with them, their superior performance is well established when the data is incomplete, noisy, and dynamic. Meanwhile, there is a renewed interest in iterative algorithms due to the improvement in computational capabilities [

Because a projection for the point x-ray source is a linear integral of attenuation values along the x-ray path (

Let

Following the same steps as for the point source, a projection for the line-shaped x-ray source based on (

Although (

Consider a hypothetical situation in which all the points along the line x-ray source serve as point x-ray sources and let

To be consistent with indexing, let us also call

To validate the feasibility of line-shaped x-ray source and demonstrate the merits of generalized SART algorithm, we developed a numerical simulator. The thorax Phantom [

Numerical simulation results are presented in Figures

Comparison of images reconstructed using line-SART algorithm using a line source of length 3 cm at different iteration numbers. (a) Original Image. Reconstructed images in (a), (b), and (c) are, respectively, at 30, 60, and 100 iterations. Display window is

Line SART reconstructed images after 100 iterations using a line source of length 3 cm at two different display windows with profiles along the dotted line. (a) Reconstructed image at a display window of

Line SART reconstructed images after 100 iterations using a line source of length 5 cm at two different display windows with profiles along the dotted line. (a) Reconstructed image at a display window of

Line SART reconstructed images after 100 iterations using a line source of length 8 cm at two different display windows with profiles along the dotted line. (a) Reconstructed image at a display window of

A point x-ray source used in commercial CT scanners limits the temporal and spatial resolution and also results in frequent heating of the x-ray tube. These limitations may be overcome by using the proposed line-shaped x-ray source based image technique. Reconstructing image from a line-shaped x-ray source is a challenging task due to nonlinear nature of the resulting projection data. In this article, we developed a generalized SART algorithm to enable reconstruction from a line source. We believe that this algorithm can be easily extended to more general 1D x-ray source shapes and even to 2D planar x-ray sources as well, which may have applications in dynamic imaging. Moreover, the OS-SART algorithms [

To the best of our knowledge, this is the first paper attempting to solve the contradiction between temporal and spatial resolutions by a nonpoint source. Additional research efforts are necessary along this direction. In this study we acquired projection data over an angular range of

There are also possibilities for enhancing our algorithm or developing new algorithms. In our view, the main limitation of our generalized SART algorithm is the blurring of the edges and a large number of iterations required to reconstruct sharp images. To this end, gradient or prior information may be incorporated within our algorithm or other algorithms utilizing gradient information could be developed in the future. Some examples of prior information include support and nonnegativity constraints [

This is a feasibility study, and there is not enough information to comment on scatter and its effects. Scattering is a real concern in computed tomography and it will become important to study the amount of scatter and resulting image degradation as the line-shaped-based x-ray source tomography advances. However, if needed, new algorithms could be developed to reduce the effects of scatter.

In conclusion, we proposed a novel line-shaped x-ray source based CT imaging technique and corresponding reconstruction method. The developed generalized SART algorithm enables image reconstruction from projection data of not only a line-shaped x-ray source but also more generalized 1D and 2D source. Our numerical simulations have demonstrated the feasibility and merits of the proposed techniques and algorithms. Some interesting future research directions were also presented.

This work was partially supported by NIH/NIBIB grants (EB002667, EB004287, and EB007288).