3D Image Reconstruction Using X-Rays for CT Scan

Computer tomography has become a major area in biomedical imaging system to reconstruct 3D image. Several exact CT reconstruction algorithms, such as the generalized filtered-back projection (FBP) and back projection-filtration (BPF) methods and cone beam reconstruction algorithm have been developed to solve the long object problem. Although the well-known 3D Shepp-Logan phantom (SLP) is often used to validate these algorithms, it is deficient due to the discontinuity of the SLP. The need for a practical method of reconstruction (i.e. performing the inverse radon transform) gave rise to the back projection technique (FBP). There are two method of filter back projection the first method back projection the measurements at each projection are projected or `smeared´ back along the same line. The other method is filtered back projection is still the standard technique in commercial scanners used to correct the blurring encountered in back projection method. A basic problem in imaging with X-rays (or other penetrating radiation) is that a two-dimensional image is obtained of a three-dimensional object. This means that structures can overlap in the final image, even though they are completely separate in the object. This is particularly troublesome in medical diagnosis where there are many anatomic structures that can interfere with what the physician is trying to see. Thus filter back projection algorithm is the easiest way to reconstruct the image. In this paper first we present FBP algorithm and then weighting scheme used in the case of helical/spiral cone-beam scanning.3 dimensional conversions of the Shepp and Logan phantom are used to test the cone beam reconstruction algorithm.