Super-resolution in Structured Illumination Microscopy (SIM) is obtained through de-aliasing of modulated raw images, in which high frequencies are measured indirectly inside the optical transfer function. Usual approaches that use 9 or 15 images are often too slow for dynamic studies. Moreover, as experimental conditions change with time, modulation parameters must be estimated within the images. This paper tackles the problem of image reconstruction for fast super resolution in SIM, where the number of available raw images is reduced to four instead of nine or fifteen. Within an optimization framework, the solution is inferred via a joint myopic criterion for image and modulation (or acquisition) parameters, leading to what is frequently called a myopic or semi-blind inversion problem. The estimate is chosen as the minimizer of the nonlinear criterion, numerically calculated by means of a block coordinate optimization algorithm. The effectiveness of the proposed method is demonstrated for simulated and experimental examples. The results show precise estimation of the modulation parameters jointly with the reconstruction of the super resolution image. The method also shows its effectiveness for thick biological samples.