Restoration of Coherent Images

In this thesis a series of novel algorithms for high quality restoration of coherent images is introduced. This task cannot be solved with established methods for the restoration of incoherent images. These algorithms focus on the correction of images in coherent imaging systems with a-priori known aberrations. The new wavefront correction algorithms achieve a significantly higher restoration quality than any previously known technique. The algorithms in this thesis are based on latest advances in optimization algorithms, particularly projections onto convex sets, proximal optimization and fractal self-similarity. Convergence and performance of the individual algorithms are analyzed in detail in various scenarios on real and simulated images. The evaluation also deals with the impact of noise on the restoration quality. Practical application of the new algorithms on microscopic images of diverse biological and human samples, as well as shadowgraph images of plankton acquired with a laboratory setup prove their efficiency. The new algorithms also have promising future applications in other areas, for example in adaptive optics and astronomy.

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