  We extend our previous three-dimensional (3D) model-based (MB) approach for
3D structured illumination microscopy (SIM) by introducing a positivity
constraint (PC) through the reconstruction of an auxiliary function using a
conjugate-gradient method. The performance of the new 3D-MBPC method is
investigated with noisy simulation and compared to our previous 3D-MB approach
and to the 3D Generalized Wiener filter approach used traditionally for 3D
processing of 3D-SIM data. Results show more accurate 3D restoration is
possible with the 3D-MBPC method over the other two methods. Moreover,
information redundancy in 3D-SIM data is exploited and results obtained with
the 3D-MBPC method when the number of raw SIM images is reduced from 15 down to
7 and 5 are promising.
