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Application of the matrix completion algorithm for compression and data processing of sea surface temperature with sparse measurement errors.

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Title: Application of the matrix completion algorithm for compression and data processing of sea surface temperature with sparse measurement errors.
Authors: Sheloput, T. O., Petrov, S. V., Kosolapov, I. A.
Source: Computational Mathematics & Modeling; Jan2024, Vol. 35 Issue 1-4, p19-28, 10p
Subject Terms: LOSSY data compression, DATA compression, OCEAN temperature, SPARSE matrices, LOW-rank matrices
Abstract: Due to the need to store and transfer an ever-increasing volume of geophysical data, the problem of developing effective compression algorithms is becoming increasingly important. In order to use geophysical data in practical applications, some preliminary processing is carried out (for example, filtration of anomalies and data interpolation). In this article, a method based on matrix approximations is applied to problems of compression, preliminary processing, and interpolation of sea surface temperature (SST). The method that we use is based on approximating the data matrix as the sum of a low-rank matrix and a sparse matrix. It is shown that it allows lossy compression of the data on sea surface temperature obtained from satellites, and it can also be used to fill in relatively small gaps in the data. The quantity of real numbers that is required to restore the approximation of the source field, depends on the permissible approximation error. In order to calculate a single element of the matrix approximation, R multiplications are required, where R denotes the rank of the matrix. The sparse component of the matrix approximation contains elements that the algorithm considers to be anomalies, and they are usually localized near the coast. A possible reason is the actual presence of anomalies in the data from coastal zones and the specifics of formation of the source matrix from the data, which may require correction. It should be noted that further numerical studies are needed to formulate recommendations for using the method for compression, processing, and data interpolation [ABSTRACT FROM AUTHOR]
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Database: Complementary Index
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Abstract:Due to the need to store and transfer an ever-increasing volume of geophysical data, the problem of developing effective compression algorithms is becoming increasingly important. In order to use geophysical data in practical applications, some preliminary processing is carried out (for example, filtration of anomalies and data interpolation). In this article, a method based on matrix approximations is applied to problems of compression, preliminary processing, and interpolation of sea surface temperature (SST). The method that we use is based on approximating the data matrix as the sum of a low-rank matrix and a sparse matrix. It is shown that it allows lossy compression of the data on sea surface temperature obtained from satellites, and it can also be used to fill in relatively small gaps in the data. The quantity of real numbers that is required to restore the approximation of the source field, depends on the permissible approximation error. In order to calculate a single element of the matrix approximation, R multiplications are required, where R denotes the rank of the matrix. The sparse component of the matrix approximation contains elements that the algorithm considers to be anomalies, and they are usually localized near the coast. A possible reason is the actual presence of anomalies in the data from coastal zones and the specifics of formation of the source matrix from the data, which may require correction. It should be noted that further numerical studies are needed to formulate recommendations for using the method for compression, processing, and data interpolation [ABSTRACT FROM AUTHOR]
ISSN:1046283X
DOI:10.1007/s10598-025-09616-0