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. When dealing with 2D data, one generally requires 9 patterned images to reconstruct a super resolved image. Reducing this number of images is essential in order to improve temporal resolution of the system. The first part of this project will consist in showing properly that 4 patterned images are in fact sufficient to reconstruct a super resolved image (consistent system of equations). Based on this analysis, the second part of the project will be devoted to the development of a direct algorithm (non-iterative) requiring only 4 input images.