Assuming the convolutional model and a known wavelet, reflectivity inversion is an ill-posed problem. Existing methods mostly regularize the problem using mathematical criterion, such as minimization of the reflectivity vector norm. We propose reflectivity inversion using atomic decomposition, in which the atoms can be basic geological structures or derived from well logs. This is equivalent to replacing mathematical criterion by geological ones. Numerical results show that atomic decomposition is robust to noise. When applied to multi-dimensional data in a trace by trace basis, atomic decomposition shows lateral instability. The solutions are non-unique. Atomic decomposition results are probable solutions, which can be laterally regularized by re-projection.