Every radioactive source can be characterized by an histogram obtained after collecting the energies of photons emitted from the source, also called energy spectrum. However, when the activity of this source is high, a physical phenomenon known as the pile-up effect distorts direct measurements, resulting in a significant distortion of the energy spectrum. We suggest in this letter an iterative algorithm to attenuate the pile-up effect and enhance the resulting energy spectra. It is based on iterations of a post-processed, non-negative, version of the Least Absolute Shrinkage and Selection Operator (LASSO). Results on simulations and real data illustrate the improvement obtained by the proposed method.