In off-axis electron holography, the information about the specimen co
ntained in amplitude and phase of the image wave is recorded by superi
mposing a reference wave to the image wave and recording the resulting
interference pattern, called a hologram, The image wave is usually re
trieved from this hologram by a filtering process in Fourier space. An
alternative approach is to calculate the image wave pixel by pixel fr
om the intensities in the hologram. In this paper, we describe a neura
l network that performs this step, As neural networks can represent no
nlinear relations between the input and output data, this reconstructi
on process can use the nonlinear part of the information contained in
the hologram and is thus less sensitive to noise.