In this talk, we consider the ill-posed inverse problem of restoring a motion-blurred image, resulting from a uniform linear camera motion. Firstly, we adapt a general probabilistic method to estimate the motion parameters. Thanks to the uniform linear assumption, the estimation of the parameters reduces to the detection of the direction and of the gap between oscillations of the Fourier spectrum. Using the Helmholtz principle, the maximum meaningful parallel alignments are detected in the frequency domain, and the direction and the extent of the blur are identified by an adapted K-means cluster algorithm. Secondly, we restore the image using a constrained total variation approach. Among all solutions generating the same observed blurred image, the method chooses one with small total variation. We conclude the talk by some experiments. On simulated motion-blurred images, the restoration is simply perfect. On natural images, the quality of the process depends whether or not the uniform linear motion blur assumption is satisfied. This suggests to generalize the approach so that this assumption may be relaxed.