The filtered back projection algorithm is one of the most important reconstruction methods in computed tomography which is based on explicit formulas for recovering mollified versions of the original unknown function.In this paper the author established the image reconstruction process by a mollification approach by recovering \(\Phi_{\alpha}*_xf\), where \((\Phi_{\alpha})_{\alpha>0}\) is a family of radially symmetric mollifiers with \(\Phi_{\alpha}*_xf\to f\). The formulas derived that recover smooth approximations \(\Phi*_xf\) of some function \(f\) from the spherical mean Radon transform \(M_f\) with centers restricted to the boundary of a ball. Such regularized back projection formulas account for noise in the measured data and serve as the basis of stable back projection-type reconstruction algorithms.