An Explicit Closed-Form Solution to the Limited-Angle Discrete Tomography Problem for Finite-Support Objects

: 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 inte- of 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 integer-tions sample values. The well-known ill-posedness of the limited angle valued) using precomputed coefficients; nowhere in the proce-tomography problem manifests itself in some very large coefficients dure ...

• Type: Conference
• Year: 1998
• Where: ICIP
• Authors: Andrew E. Yagle
• Keywords: Finite Support Object, ICIP 1998, Image Processing, Object Sample Values, Projections Ger Values