A matrix completion method

Abstract

The invention relates to a high precision matrix completion method based on low-rank approximation. In actual use, large-scale data are often needed in fields such as image processing, commodity recommendation systems and magnetic resonance spectroscopy. Collection of large-scale data requires a lot of time. One way is to accelerate data collection by collecting partial signals and to recover complete signals based on low-rank characteristics of the data. The method comprises the steps of approximately calculating the rank of a matrix by using an approximation function, building a rebuilding model for missing signals of the matrix and finally rebuilding the signals through an iterative algorithm. A rebuilt matrix is high in precision, the operation is easy, and the method can recover complete signals from a small amount of data.

Description

technical field [0001] The invention relates to a matrix completion method, in particular to a high-precision matrix completion method based on low-rank approximation. Background technique [0002] In many practical applications, such as image processing, commodity recommendation systems, and magnetic resonance spectroscopy, etc., in the actual sampling process, due to limitations of hardware and physical conditions, the sampling speed has to be accelerated, so the actual data obtained is not complete or The expected resolution is not achieved, and missing parts of the acquired data need to be reconstructed. Especially in the field of high-dimensional applications, the amount of data is usually very large, and the full sampling time is too long. Non-uniform undersampling is often used to shorten the sampling time during measurement, and complete data and expected resolution are obtained through reconstruction. The original matrix can be restored by using the high-dimensiona...

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Problems solved by technology

However, undersampling can easily cause spectral peaks to overlap and form spurious peaks

In order to obtain high-quality spectra, undersampled data can be reconstructed through the self-sparse nature of the spectra (Xiaobo Qu, Xue Cao, Di Guo, Zhong Chen, "Compressed sensing for sparse magnetic resonance spectroscopy," International Society for Magnetic Resonance in Medicine 19th ScientificMeeting.Stockholm, Sweden, pp.3371, 2010.); the reconstruction can be realized by using the low-rank property of the Hankel matrix corresponding to the time-domain signal of magnetic resonance spectroscopy (Xiaobo Qu, Maxim Mayzel, Jian-Feng Cai, Zhong Chen, Vladislav Orekhov."Accelerated NMR spectroscopy with low-rank reconstruction,"Angewandte Chemie International Edition,vol.54,no.3,pp.852-854,2015.), but these methods do not perform well at low sampling rates

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