The purpose of this thesis is to develop a mathematical approach and associated software implementation for deconvolution of two-dimensional Transmission Electron Microscope (TEM) images. The focus is on TEM images of weakly scattering amorphous biological specimens that mainly produce phase contrast. The deconvolution is to remove the distortions introduced by the TEM detector that are modeled by the Modulation Transfer Function (MTF). The report tests deconvolution of the TEM detector MTF by Wiener _ltering and Tikhonov regularization on a range of simulated TEM images with varying degree of noise.The performance of the two deconvolution methods are quanti_ed by means of Figure of Merits (FOMs) and comparison in-between methods is based on statistical analysis of the FOMs.