Efficient reduction of Computed Tomography problems to the developed problem of recovery functions in the form of a finite convolution in the norms of "flexible" Hilbert Sobolev and Sobolev-Radon spaces according to the scheme of the Computational (numerical) diameter

Computed tomography is a vital need to know the structure of inside body from information obtained its transillumination without destroying shell. The format presented here forsolving this massively understandable problem, which can only be theoretical and mathematical with subsequent engineering implementation, fundamentally expressed in approximate formula established by authors 2019 on plane two-dimensional Cartesian coordinate system. In article,this breakthrough brought complete surprise equivalence fundamental problems Tomography both widely known developed new content continuations recovery functions operators form finite convolution values approximated at grid nodes specially constructed kernels: \[sup\left\{{\left\|f\left(x\right)-\sum^N_{k=1}{{\left(R^2\right)}^{-1}Rf\left({\xi }_k\right)}R\left(\textrm{Ф}\left(y-{\xi }_k\right)\right)(x)\right\|}_{W^{{\left\|y\right\|}^{\frac{s-1}{2}}}_2\left(S^{s-1}\times R^1\right)}: f\in W^{әlpha \left(y\right) \cdot{\left\|y\right\|}^{\frac{s-1}{2}}}_2\left(S^{s-1}\times R^1\right)\right\}әsymp \] \[әsymp sup\left\{{\left\|f(x)-\sum^N_{k=1}{f\left({\xi }_k\right)}\textrm{Ф}(x-{\xi }_k)\right\|}_{L^2\left(E_s\right)}: \left(y\right)}_2\left(E_s\right)\right\},\] As customary Mathematics (in other sciences too), any claim for must demonstratedin results importance. resulting equivalence, working part turned out astate enough illustrative and, necessary, conclusions readiness according ComputerScience offered first author (according list) 1996 filled Kazakhstan far trivialcontent Computational (numerical) diameter (C(N)D). Namely, wide range developments thetheory C(N)D instantly automatically leads direct practical applications advances Tomography, including analytic expressibility explicit formulas computational aggregates terms scanned quantities. Among them also conclusion that Tomographythere no better scanning method than Radon transform.