Magnetic Resonance Imaging (MRI) is a technique used to obtain, in the form of a picture, information about structure, composition and even functionality of an object. It is characterized by its high reproducibility, accuracy and versatility, and it offers high spatial resolution, wide field-ofview and good contrast between soft tissues. However, MRI presents some disadvantages: it is slow compared to common physiological processes such as blood flow, heartbeat or breath hold and, in addition, it is very sensitive to motion.A common approach to accelerate MRI acquisitions is to collect only a portion of k-space (subsampling) and to apply advanced image processing techniques for image reconstruction. Nevertheless, the problem to be solved becomes undetermined and ill-conditioned. Thus, some knowledge, constraints and assumptions are added to the information of the image model to define a cost function, the optimization of which provides a regularized solution. This Thesis deals with the computationally demanding problem of dynamic MRI reconstruction from highly undersampled data. The motion present in the dynamic sequence is used as a complementary source of knowledge to exploit conveniently the redundancies existing in both temporal and spatial dimensions. On one hand, this Thesis explores spatially varying regularization terms that take into account motion to weight pixelwise the amount of regularization needed. On the other hand, we have proposed what we call the elastic aligned-SENSE (EAS) solution, in which a motion-free pattern image, together with a set of nonrigid deformations, are the results of our optimization. xiii xivThe pattern image is deformed to the corresponding phase of the cardiac cycle to build the CINE sequence. In terms of computational needs, our results are less demanding than other methods that make use of motion to foster sparsity. However, occasionally motion is lost in some areas of the image. This is due to the fact that the method is model-based and in such methodologies performance is satisfactory as long as the model describes accurately the motion that is being dealt with. In fact, through-plane movement makes estimated motion not represent the real deformations that the heart undergoes and thus quality of reconstructions is compromised.Therefore, the extension to 3D seems a natural future line of research.EAS computational performance makes it specially suitable as a fast initializer for other data-driven motion-compensated compressed sensing methods that make use of motion for smart regularization. This makes motion not as critical as when it is used in the image forward model -as it is the case of EAS-but EAS does provide those methods with a convenient initial motion estimation with affordable computational load. Hence, in this new scenario, the quality of final reconstructions is maintained while execution time is considerably reduced.Additionally, a methodology based on cross validation to establish the value of the regularization parameters has been proposed, together with ...