Simultaneous Algebraic Reconstruction Technique (SART): A superior implementation of the ART algorithm

Abstract

In this paper we have discussed what appears to be a superior implementation of the Algebraic Reconstruction Technique (ART). The method is based on 1) simultaneous application of the error correction terms as computed by ART for all rays in a given projection; 2) longitudinal weighting of the correction terms back-distributed along the rays; and 3) using bilinear elements for discrete approximation to the ray integrals of a continuous image. Since this implementation generates a good reconstruction in only one iteration, it also appears to have a computational advantage over the more traditional implementation of ART. Potential applications of this implementation include image reconstruction in conjunction with ray tracing for ultrasound and microwave tomography in which the curved nature of the rays leads to a non-uniform ray density across the image.

Tomographic diagnostic of the hydrogen beam from a negative ion source

“…In order to solve the inverse problem of the tomography in SPIDER, two methods have been considered so far: the SVD [17,20] and the algebraic reconstruction technique (ART) [18,[21][22][23], in particular in its modified form called simultaneous algebraic reconstruction technique (SART) [24]. The SART technique has been preferred to the SVD because it gives better results when noisy data are used, as described also in the cited references.…”

Fast laboratory-based micro-computed tomography for pore-scale research: Illustrative experiments and perspectives on the future

“…when enough projections are acquired). In the context of (dynamic) CT imaging, iterative reconstruction techniques [46,47] have gained much interest. During iterative reconstruction, intermediate solutions of the reconstructed 3D object are incrementally refined by simulating projection images from this solution (by forward projection) and subsequently adapting it to better reproduce the experimental projections.…”

Ghosts in Discrete Tomography

“…In fact, we can easily see that, for each choice of n ∈ F − S , the point (a, b) = (2, 2) − n does not satisfy conditions (9) or (10) (or both), so that its multiplicity cannot be reduced without adding new multiplicities as asked in Problem 1. Now we give an example in which Algorithm 3 returns a solution.…”

“…For instance, in Example 3, a further possible reduction is given by A complete reduction can be obtained, for instance, just adding K(x, y) = 1 + x 2 Y 4 to H(x, y). In fact, according to Proposition 3, the pair (0, 0) can be selected for the multiple points (2, 3), (2,4), (3,5), (3,6), (3,8), (3,9), (4,11), and the pair (2, 4) can be selected for the multiple points (3,5), (3,7), and (4,10 As a further remark, we point out that, in view of Theorem 1, which is valid for any choice S, the same Algorithm 3 can be applied to set S of higher cardinality, up to checking conditions (C) for any possible multiple point of F S .…”

“…A main problem for a correct image understanding is the localization of such sub-pictures. The same problem arises when FBP is replaced by algebraic reconstruction algorithms, such as ART, SART or SIRT, which usually supply more accurate results in case that only a few projection angles are available (see, for instance [6,9,10]). In principle, any algebraic-based reconstruction algorithm, cannot "see" sets having null projections along each one of the employed X-ray directions.…”