Abstract : The present report summarizes the research activities that I have carried out since completion of my PhD. My attention has focused on the fundamental signal processing problem of source signal estimation from the observation of corrupted measurements, in scenarios where the measured data can be considered as unknown linear transformations of the sources. Two typical problems of this kind are the deconvolution or equalization of channels introducing linear distortions and source separation in linear mixtures. The blind approach makes as few assumptions as possible about the problem in hand: these typically reduce to the statistical independence of the sources and the invertibility of the channel or mixing matrix characterizing the propagation medium. Despite the advantages that have driven the interest in these techniques since the 70's, blind criteria also present some important drawbacks such as the existence of estimation ambiguities, the presence of local extrema leading to spurious solutions, and a high computational complexity often linked to slow convergence. My research has been devoted to the design of novel signal estimation techniques alleviating the drawbacks and thus improving the performance of the blind approach. Special emphasis has been laid on two specific applications in telecommunications and biomedical engineering: equalization and source separation in digital communication channels and atrial activity extraction in surface electrocardiogram recordings of atrial fibrillation patients. Most of the proposed techniques can be considered as semi-blind in that they aim at exploiting available prior information about the problems under study other than source independence; e.g., the existence of training data in communication systems or specific properties about the atrial source in atrial fibrillation. In communications, the approaches that I have explored include algebraic solutions to contrast functions based on digital modulations, the combination of blind and training-based contrasts into semi-blind criteria, and an iterative optimization technique with an optimal step-size coefficient computed algebraically. Our efforts to extract the atrial signal in multi-lead atrial fibrillation recordings has led not only to new contrast functions based on second- and higher-order statistics incorporating priors about the source statistics, but also to novel results of clinical and physiological significance about this challenging cardiac condition. The report concludes by proposing some possible avenues for the continuation of this work. This investigation has been carried out in collaboration with a number of colleagues in France and abroad, and has also comprised the joint supervision of several PhD students. The resulting contributions have given rise to over sixty publications in international journals, conferences and book chapters. A compilation of selected publications is attached to this document.