Structured Illumination Microscopy (SIM) allows us to improve the resolution of classical wide-field imaging systems by moving high-frequency components into the observable microscope region. This microscopy technique relies on patterned illuminations of the sample to produce super-resolution images. As a result, pattern calibration conditions the reconstruction performance and reconstruction artefacts are often due to an inaccurate knowledge of these patterns. However, patterns are generally partially known up to a parametric model whose parameters remain unknown. The objective of this project is thus to develop a reconstruction algorithm in order to jointly estimate patterns model parameters and the super-resolved volume. To this end, the student will benefit from the Matlab inverse problem library developed in out group (http://bigwww.epfl.ch/algorithms/globalbioim/).