Study of three-dimensional volume image reconstruction and its application to positron emission tomography

Abstract

The continuous efforts to achieve higher quality imaging in computerized tomography (CT) results in extension of the algorithm for conventional 2-D reconstruction to direct three-dimensional volume reconstruction. A generalized true three-dimensional reconstruction (GTTR) algorithm which is applicable to both conventional 2-D reconstruction and direct volume reconstruction for complete sphere, as well as truncated sphere, geometry is proposed. This algorithm is based upon the filtered backprojection method which is considered to provide both computational efficiency and highly quantitative image in the digital computer application. This particular algorithm facilitates the partial volume image reconstruction of an elongated object, such as the human body, which is imperative to the medical application. A new image synthesizing method using the image focusing concept, which is one of the characteristics of this algorithm, is suggested. Three-dimensional volume image reconstruction requires two-dimensional signal processing of projection data. The calculation error and its reducing method, which comes from digital filtering in the Discrete Fourier domain, is considered. A derivative weighting function is proposed to minimize the ringing artifacts resulting from the boundary slope discontinuity of the filter function. In addition to the proposed GTTR algorithm the 2-D and 3-D reconstruction algorithms and the characteristics of each are considered systematically. The filtered backprojection and 3-D cone-beam reconstruction algorithms are studied in detail in order to show the applicability to practical image reconstruction.