The rapid development of high-brilliance X-ray sources in the last decade has opened the way to extremely powerful imaging modalities. Third generation synchrotron sources and newly built X-ray free-electron lasers offer a very high flux and can produce X-ray beams with excellent coherence properties. Imaging techniques that rely on the coherence of the incoming field can give access to phase contrast signal, known to be much stronger than absorption in the hard X-ray regime, and even make possible lensless imaging, thus offering the potential for very high-resolutions. To make the most of X-ray's high penetration power, it is best to combine these novel imaging approaches with computed tomography to achieve high-resolution, high-sensitivity 3D imaging.The goal of this project is to break new ground in coherence-based imaging primarily through new developments in data analysis techniques. My group will work on a variety of novel or improved reconstruction approaches that will push the potential of these methods to their limit in resolution, sensitivity and usability, an objective well summarized by the term ``optimal imaging'' in the title of this proposal.The main sub-projects described in this proposal are: (1) developing, improving and validating ptychographic reconstruction methods; (2) combining tomography and ptychography, and applying it to life and materials science samples; (3) developing efficient and robust tomographic reconstruction algorithms for grating interferometer imaging; and (4) implementing efficient data-analysis pipe-lines for future X-ray free-electron laser experiments.