The prime motivation of this work is to devise techniques that make the algebraic reconstruction technique (ART) and related methods more efficient for routine clinical use, while not compromising their accuracy. Since most of the computational effort of ART is spent for projection/backprojection operations, we first seek to optimize the projection algorithm. Existing projection algorithms are surveyed and it is found that these algorithms either lack accuracy or speed, or are not suitable for cone-beam reconstruction. We hence devise a new and more accurate extension to the splatting algorithm, a wellknown voxel-driven projection method. We also describe a new three-dimensional (3-D) ray-driven projector that is considerably faster than the voxel-driven projector and, at the same time, more accurate and perfectly suited for the demands of cone beam. We then devise caching schemes for both ART and simultaneous ART (SART), which minimize the number of redundant computations for projecti...

Abstract—The mathematical problem posed by Computed Tomography (CT), which includes projecting radiation through an object resulting in an estimate of this object’s interior, is to calculate image data (the pixel values) from the projection values. Although for now the filtered back-projection algorithm is most widely used by manufacturers, efforts are being made to make iterative methods popular again due to their unique advantages, such as their performances with incomplete noisy data. The algebraic reconstruction technique (ART), the simultaneous algebraic reconstruction technique (SART) and the simultaneous iterative reconstruction technique (SIRT) are a few of those iterative methods and in this paper we discuss these techniques and how they can be implemented in MATLAB, a numerical computing environment and programming language, created by The MathWorks. We begin by creating the weight matrix. This is the matrix which holds the importance indicators per pixel. Then we move on to the actual reconstructions and we end by implementing these algorithms and calculations in a graphical user interface. I.

3D computed tomography has been extensively studied and widely used in modern society. Although most manufacturers choose the filtered backprojection algorithm (FBP) for its accuracy and efficiency, iterative reconstruction methods have a significant potential to provide superior performance for incomplete, noisy projection data. However, iterative methods have a high computational cost, which hinders their practical use. Furthermore, regularization is usually required to reduce the effects of noise. In this paper, we analyze the use of the Simultaneous Algebraic Reconstruction Technique (SART) with total variation (TV) regularization. Additionally, graphics hardware is utilized to increase the speed of SART. NVIDIA’s GPU and Compute Unified Device Architecture (CUDA) comprise the core of our computational platform. GPU implementation details, including ray-based forward projection and voxel-based backprojection are illustrated. Experimental results for high-resolution synthetic and real data are provided to demonstrate the accuracy and efficiency of the proposed framework. 1

Accurately reconstructing the three-dimensional mass shapes in mammographic images is important for classifyingtheabnormalityintomalignantorbenign.Inthispaper,a partial volume compensated reconstruction technique for mass shapes is presented. The two-dimensional shapes of themassesarefirstautomaticallysegmentedusingaregion growingapproach.The3Dmassshapesaretheniteratively refinedaccordingtoanalgebraicreconstructiontechnique. Partialvolumeestimationisappliedontheboundarytogeta smoother 3D shape. Evaluation results show that the proposed algorithm improves the accuracy of the mass reconstruction. KEY WORDS: 3D reconstruction, mass shape, mammography, partial volume effect, region growing