Abstract
Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application of SVD in recovering ripped photos was exploited. Recovery was done by applying truncated SVD iteratively. Performance was evaluated using the Frobenius norm. Results from a few experimental photos were decent.
Highlights
Singular value decomposition is a matrix decomposition that decomposes or factorizes a matrix as a product of three component matrices
Singular value decomposition always appears in problems that entail analysis of large amount of data because data often comes in the form of matrix
The application of Singular value decomposition (SVD) has been well known in principal component analysis, data and image compression, and in solving least square problems via pseudoinverse [2,3,4]
Summary
Singular value decomposition is a matrix decomposition that decomposes or factorizes a matrix as a product of three component matrices. It was established ways back in the 19th century due to the contributions by Eugenio Beltrami, Camille Jordan, James Joseph Sylvester, Erhard Schmidt, and Hermann Weyl [1]. Singular value decomposition always appears in problems that entail analysis of large amount of data because data often comes in the form of matrix. The application of SVD has been well known in principal component analysis, data and image compression, and in solving least square problems via pseudoinverse [2,3,4]. Application of truncated SVD in ripped photos recovery is not widely reported in the literature
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