The matrix completion problem considers a matrix in which some elements are unknown. The goal is to determine the elements, such that the rank of the filled matrix is minimal. In this thesis, we present the theoretical background of five different algorithms used to solve this problem (NNM, SVT, TNNM, ASD, LMaFit) and test them. In testing, we focus on the reconstruction of images where the values of some pixels are unknown. We analyze different aspects of reconstructions and interpret the results referring to the mathematical background of the algorithms. We also compare the results with a more standard method of image reconstruction, based on solving the Laplace differential equations.
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