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We extend our previous three-dimensional (3D) model-based (MB) approach for3D structured illumination microscopy (SIM) by introducing a positivityconstraint (PC) through the reconstruction of an auxiliary function using aconjugate-gradient method. The performance of the new 3D-MBPC method isinvestigated with noisy simulation and compared to our previous 3D-MB approachand to the 3D Generalized Wiener filter approach used traditionally for 3Dprocessing of 3D-SIM data. Results show more accurate 3D restoration ispossible with the 3D-MBPC method over the other two methods. Moreover,information redundancy in 3D-SIM data is exploited and results obtained withthe 3D-MBPC method when the number of raw SIM images is reduced from 15 down to7 and 5 are promising.

3D model-based restoration with positivity constraint using a reduced number of 3D-SIM images