Radiation detectors often work at high count rates, therefore experiencing a high fraction of pileup. Pileup is the situation of two or more pulses partly or completely overlapping. Pileup effects cause that the energy of each single pulse is harder to be precisely obtained at high count rates. Consequently, it makes the energy resolution (ER) of the detector system degenerate. In this paper, we propose an expectation maximization deconvolution (EMD) method for processing pileup events and recovering the energy of each single pulse. EMD not only has non-negative property and energy conservation, but is independent of the pulses shape. We employ this method to recover pileup events accurately in iteration formation. Specifically, in this method, we first derived an event pulse function to express the average scintillation pulse, then the pileup events signal is constructed as a convolution model. Based on this convolution model, we solve the problem using EM iteration. Lastly, energies are calculated from the separated pulse after EM iteration. To evaluate the performance of EMD, we set up one gamma ray detector utilizing an LYSO crystal and a CR105 photomultiplier tube (PMT). Scintillation pulses are directly read out by a digital storage oscilloscope with high sample rates. For single pulses, measured energies using our EMD method are almost equal to that of the digital gate integrator (DGI). For pileup pulses, the ER obtained by EMD, DGI and the digital delay-line clipping (DDLC) is 16.31%, 29.05%, 19.08% at 511keV, respectively, which illustrates EMD is obviously preferable to that of well-established methods.