Determination of range conditions for general projection pair operators
Abstract
Abstract In the context of tomographic imaging, a projection is a set of line integrals over a collection of curves. This work discusses the range of tomographic ‘projection pair operators’ P consisting of two such projections. We restrict our investigations to a planar setting (operators that act on functions in R 2 ). Range conditions for P can be associated with the set of annihilators of Rg ( P ) . We find that this set of annihilators contains at most one dimension, and the corresponding range conditions can be explicitly determined by what we refer to as ‘kernel conditions’. With this tool, we show that under certain assumptions, the exponential fanbeam projection pair operator has dense range.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Digital Image Processing Techniques
Medical Image Segmentation Techniques
Publication details
- Journal / source
- Inverse Problems
- Volume
- 42
- Issue
- 3
- Pages
- 035007–035007
- Publication date
- 2 March 2026
- Language
- EN