| Summary: | Let <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> represent a digitized version of an image <inline-formula> <tex-math notation="LaTeX">$f\left ({x,y }\right)$ </tex-math></inline-formula>. Assume that the image fits inside a rectangular region and this region is subdivided into <inline-formula> <tex-math notation="LaTeX">$M\,\,\times \,\,N$ </tex-math></inline-formula> squares. We call these squares the shifted box functions. Thus <inline-formula> <tex-math notation="LaTeX">$f\left ({x,y }\right)$ </tex-math></inline-formula> is approximated by <inline-formula> <tex-math notation="LaTeX">$M\,\,\times \,\,N$ </tex-math></inline-formula> matrix <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula>. This paper proofs that <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula> can be recovered exactly and uniquely from the Radon transform of <inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> using only one selected view angle with a well selected family of <inline-formula> <tex-math notation="LaTeX">$MN$ </tex-math></inline-formula> 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.
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