%0 Journal Article
%T Prior Image Guided Undersampled Dual Energy Reconstruction with Piecewise Polynomial Function Constraint
%A Dufan Wu
%A Li Zhang
%A Liang Li
%A Le Shen
%A Yuxiang Xing
%J Computational and Mathematical Methods in Medicine
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/437917
%X Dual energy CT has the ability to give more information about the test object by reconstructing the attenuation factors under different energies. These images under different energies share identical structures but different attenuation factors. By referring to the fully sampled low-energy image, we show that it is possible to greatly reduce the sampling rate of the high-energy image in order to lower dose. To compensate the attenuation factor difference between the two modalities, we use piecewise polynomial fitting to fit the low-energy image to the high-energy image. During the reconstruction, the result is constrained by its distance to the fitted image, and the structural information thus can be preserved. An ASD-POCS-based optimization schedule is proposed to solve the problem, and numerical simulations are taken to verify the algorithm. 1. Introduction Computed tomography has become an important nondestructive detection method in medicine, industry, and security. Typically CT scans the object by a single energy to reconstruct the attenuation factors in order to evaluate the density distributions inside the test object. However, some materials¡¯ attenuation factors are close and hard to distinguish, which brings trouble for diagnosis. Since the attenuation factors are different under different X-ray energies, DECT [1] has been brought about to enhance the material distinguishing ability in CT. Furthermore, atomic numbers, electron densities, or specific material equivalent densities can also be reconstructed from DECT for better visualization. In DECT, the test object is scanned under different energies while keeping the object fixed. Thus, two different images, the low-energy image and the high-energy image can be reconstructed independently from the two sets of projections, the low-energy projections and the high-energy projections . Although there are various techniques for DECT reconstruction, for example, prereconstruction [2], postreconstruction [3], and iterative reconstruction [4], we concentrate on reconstructing and in this paper to demonstrate the mathematics of our method. Dose has been concerned more and more recently with the increasing public awareness of the possible risks brought about by the radiation of CT scans. One of the most efficient ways to reduce dose is to reduce the sampling number. According to the concept of compressed sensing (CS) [5, 6], when the sampling numbers are reduced beneath the conventional required sampling rate, one can still accurately recover the signal by incorporating prior knowledge to the
%U http://www.hindawi.com/journals/cmmm/2013/437917/