MRI is a non-invasive imaging modality. The main disadvantage of MRI is the time required to produce images. The time-consuming scanning process decreases the patient comfort and increases the number of artifacts caused by the patient movement. There are some possibilities to improve the imaging speed. For instance, we can speed up the scanning process by taking fewer measurements. Unfortunately, then we also lose some information. This motivates us to find fast algorithms that are able to recover lost information. In this talk I am going to introduce briefly the setting of my work. I will also show the results obtained by one of the algorithms developed to do the reconstruction.