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Magnetic resonance imaging is a very powerful tool for imaging structures or organs of the human body in a non-invasive manner. Having collected the raw data and discretized in the k-space, Fourier methods are the natural choice to reconstruct the MRI images. In this paper, a technique to reconstruct MRI images is presented. It does not perform the inverse Fourier transform directly on the k-space images. It is based on the SVD decomposition in the least square sense. This approach is compared with other existing approaches using different criteria such as the root mean square and the performance test. The results show that the proposed approach is much better.