Image reconstruction techniques are used to create 2-D and 3-D images from sets of 1-D projections. These reconstruction techniques form the basis for common imaging modalities such as CT, MRI, and PET, and they are useful in medicine, biology, earth science, archaeology, materials science, and nondestructive testing.
The mathematical foundation for these reconstruction methods are the Radon transform, the inverse Radon transform, and the projection slice theorem. Computational techniques include filtered backprojection and a variety of iterative methods. Several projection geometries are commonly used, including parallel beam, fan beam, and cone beam. The Shepp-Logan phantom image is often used to evaluate different reconstruction algorithms.
You can perform image reconstruction with Image Processing Toolbox™, which includes the most common image reconstruction algorithms. The toolbox is an add-on to MATLAB®, an environment for data analysis, visualization, and algorithm development.