New formulas for the inversion of the Radon transform

For the integral Radon transform, classical formulas for inversion of the integrand function are known, provided that it is smooth. However, this restriction does not fully correspond to the application of the results in sounding theory, which is the main area of application of the Radon transform. It would be more natural to assume that discontinuities of the first kind are admissible for integrands. The paper presents a number of inversion formulas proved by the authors for piecewise continuous functions. A comparison of the obtained formula variants is carried out and preliminary recommendations on their use for numerical algorithms are given.