To directly image an Earth-like planet orbiting another star, coronagraphs would have to suppress the light from that star to within one part per ten billion. Such observations would have to be carried out from space and even then, the images will be extremely sensitive to structural and thermal fluctuations in the optical elements of the telescope. With just tens of photons reaching each detector during a single exposure, sensing time variations in the residual starlight (speckles) and discerning them from planets proves to be a challenging task. This thesis describes algorithms for estimating the speckles both during the observations and in post-processing. It states these estimation problems in terms of the electric field rather than the intensity of the light, which then become non-linear and high-dimensional. On the other hand, this approach allows taking into account the influence of deformable mirrors, and seamlessly incorporating probabilistic and reduced-order formulations for the underlying optimization tasks.

This thesis also present numerical simulations of a realistic model of a space coronagraph in various observation scenarios. They suggest that it is possible to continuously maintain a high image contrast even when pointing at a dim star. Moreover, employing a reduced-order model of the electric field allows increasing the accuracies of both online and offline estimators without increasing their time complexity. Under favorable conditions, the corresponding planet detectability thresholds lie within less than an order of magnitude of the instrument's theoretical limits.