• The reduction of CIT approach to FBP algorithm. • The rapid 2-D CIT algorithm of electron density profile. • The possibility of detection small ionospheric irregularities. The usage of a satellite cluster of satellite-to-satellite sounding of the ionosphere makes it possible to obtain the global height distribution of an electron density between 200 and 500 km height range in the orbital plane of the cluster. This paper introduces a novel rapid two-dimensional ionospheric radio tomography algorithm that uses total electron content (TEC) data measured between low Earth orbit (LEO) satellites. This algorithm reduces the problem of the ionospheric radio tomography to the rapid filtered back-projection (FBP) algorithm, which was not previously used in the computerized tomography of the ionosphere, and which allows to obtain a high resolution nowcast. Data sets of TEC measurements were simulated via IRI-2016 model and used as an input for the developed algorithm. The reconstructed profiles of the electron density were compared with those profiles from IRI-2016 model to calculate the difference between them. The obtained accuracy is comparable to the accuracy of algebraic reconstruction algorithms (ART), which are classical in the ionospheric radio tomography, and makes it possible to use the developed method to detect local disturbances in the ionosphere that is demonstrated on a test case in this paper.