Bases compressees et probleme inverse: Application a l'imagerie photo-acoustique.

摘要

Photo-acoustic imaging has been developed for different purposes but recent years has seen the modality gain interest with applications to small animal inaiging. As a technique it is sensitive to endogenous optical contrast present in tissues and, contrary to diffuse optical imaging, it promises to bring high resolution imaging for in vivo studies at mid-range depths (3mm--10mm). Because of the limited amount of radiation tissues can be exposed to, existing reconstruction algorithms for circular tomography require a great number of measurements and averaging, implying long acquisition times. Time-resolved photo-acoustic imaging is therefore possible only at the cost of complex and expensive electronics.;Reducing the number of measurements translates directly in the possibility of reducing the nmnber of detectors in the imaging system, which means a lower fabrication cost. On the other hand, if this number of detector is kept constant, the compressed sensing approach provides a better image reconstruction or a higher frame rate.;This thesis suggests a new reconstruction strategy using the compressed sensing formalism which states that a small number of linear projections of a compressible image contain enough information for reconstruction. By directly sampling the image to recover in a sparse representation, it is possible to dramatically reduce the number of measurements needed for a given quality of reconstruction. In given configurations, this number is reduced five-fold in comparison with the literature gold-standard.