Atmospheric correction is a necessary step in image processing data and spectra recorded by spaceborne sensors for pure cloudless atmosphere, primarily in the visible and near-IR spectral range. We have present a fast and sufficiently accurate method of atmospheric correction based on the proposed analytical solutions describing with high accuracy the spectrum of outgoing radiation at the top boundary of the cloudless atmosphere. This technique includes the model of the atmosphere and its optical parameters that are important in terms of radiation transfer. The solution of the inverse problem for finding unknown parameters of the model is carried out by the method of non-linear least squares (Levenberg-Marquardt algorithm) for an individual selected pixel of the image (its spectrum), taking into account the adjacency effects. Using the found parameters of the atmosphere and the average surface albedo, assuming homogeneity of the atmosphere within a certain area of the hyperspectral image (or the whole frame), the spectral albedo at the Earth's surface is calculated for all other pixels. It is essential that the procedure of the numerical simulation with non-linear least squares of the direct transfer problem is based on using analytical solutions, which provides a very short calculation time of the atmospheric parameters (seconds or less) and the ability to perform atmospheric correction "on-fly." Testing methods of atmospheric correction was performed using the synthetic outgoing radiation spectra at the top of the atmosphere (TOA), obtained by numerical simulation in the LibRadTran code, as well as spectra of real space images of the Hyperion hyperspectrometer. A comparison with the results of atmospheric correction in module FLAASH of ENVI package has been performed. Finally, to validate our data obtained by the SHARK method, a comparative analysis with ground-based measurements of Radiometric Calibration Network (RadCalNet) was carried out.