In this thesis, we address the problem of matrix completion, where the goal is to recover missing values in a matrix based on the available data and minimizing the rank of the matrix. We focus on an algorithm that relies on Riemannian manifold techniques. In the work, we implement the algorithm presented in the paper "Low-rank matrix completion by Riemannian optimization" and test its reconstruction quality on synthetic data and on various image data with added disturbances, noise, or missing pixels. The results are then analyzed and interpreted with the help of the mathematical background of the algorithm.
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