  Measurements of transverse profiles using Ionization Profile Monitors (IPMs)
for high brightness beams are affected by the electromagnetic field of the
beam. This interaction may cause a distortion of the measured profile shape
despite strong external magnetic field applied to impose limits on the
transverse movement of electrons. The mechanisms leading to this distortion are
discussed in detail. The distortion itself is described by means of analytic
calculations for simplified beam distributions and a full simulation model for
realistic distributions. Simple relation for minimum magnetic field scaling
with beam parameters for avoiding profile distortions is presented. Further,
application of machine learning algorithms to the problem of reconstructing the
actual beam profile from distorted measured profile is presented. The obtained
results show good agreement for tests on simulation data. The performance of
these algorithms indicate that they could be very useful for operations of IPMs
on high brightness beams or IPMs with weak magnetic field.
