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SVD-Compression of Incomplete Matrices and its Applications

Student: Andrei Moiseev

Supervisor: Roman Avdeev

Faculty: Faculty of Computer Science

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2019

Image restoration is currently one of the most popular and relevant problem. This paper focuses on the graphic images which information may be lost during transmission. The image corresponds to some real-valued matrix where the unknown parts correspond to the unknown entries of the matrix. The main goal of this study is to develop and to implement a fast and effective algorithm in order to complete a partially prescribed matrix. As a possible solution we propose a method of matrix completion when the minimal rank of the filled matrix is obtained. This paper includes the description of chosen modifications and the results of tests with real partially prescribed pictures being restored with the proposed method.

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