An explicit closed-form solution to the limited-angle discrete tomography problem for finite-support objects
✍ Scribed by Andrew E. Yagle
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 101 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0899-9457
No coin nor oath required. For personal study only.
✦ Synopsis
An explicit formula is presented for reconstructing a This article derives an explicit formula for the integer values finite-support object defined on a lattice of points and taking on inteof a finite support object, defined on a lattice, from its projections ger values from a finite number of its discrete projections over a (Radon transform) at a finite number of angles over a limited limited range of angles. Extensive use is made of the discrete Fourier range. It does not require the solution of a linear system of equatransform in doing so. The approach in this article computes the tions, and it is not iterative. The formula expresses the object object sample values directly as a linear combination of the projecvalues as linear combinations of the projection values (all integertions sample values. The well-known ill-posedness of the limited angle valued) using precomputed coefficients; nowhere in the procetomography problem manifests itself in some very large coefficients dure is even a division required. This provides the following in these linear combinations; these coefficients (which are computed advantages over previous approaches: off-line) provide a direct sensitivity measure of the reconstruction samples to the projections samples. The discrete nature of the problem implies that the projections must also take on integer values;
- The solution of an large ill-posed linear system of equations this means noise can be rejected. This makes the formula practical.