Computed Tomography Reconstruction Using Only One Projection Angle

Abstract

Let $F$ represent a digitized version of an image $f\left ({x,y }\right)$ . Assume that the image fits inside a rectangular region and this region is subdivided into $M\,\,\times \,\,N$ squares. We call these squares the shifted box functions. Thus $f\left ({x,y }\right)$ is approximated by $M\,\,\times \,\,N$ matrix $F$ . This paper proofs that $F$ can be recovered exactly and uniquely from the Radon transform of $f$ using only one selected view angle with a well selected family of $MN$ lines. The paper also proposes a precise method for computing the Radon transform of an image. The approach can be categorized as an algebraic reconstruction, but it is merely a theoretical contribution for the field of limited data tomography.

Keywords

• Algebraic reconstruction
• radon transform
• tomography
• limited data tomography