High-dimensional exponential signal data completion method

Abstract

The invention discloses a high-dimensional exponential signal data completion method, and relates to a prediction and completion method of high-dimensional data. The method comprises the following steps: modeling for a high-dimensional exponential signal according to tensor parallel factorization; establishing a high-dimensional data completion model based on the tensor parallel factorization; solving the high-dimensional data completion model based on the tensor parallel factorization; post-processing the data, performing Fourier transformation on the obtained high-dimensional exponential signal to obtain a completed high-dimensional exponential signal frequency spectrum. The precision is high so that a complete signal can be completed from a small number of data. In the practical application, if a target function can be modeled as the high-dimensional signal of an exponential function, through the adoption of the high-dimensional exponential signal completion method, the small number of data can be used for completing to obtain the complete signal, thereby achieving the aims of overcoming the limitation of a sampling apparatus, reducing the sampling time and improving the resolution of the frequency spectrum.

Description

technical field [0001] The invention relates to prediction and completion of high-dimensional data, in particular to the problem of data completion of high-dimensional signals with exponential functions. Background technique [0002] In many practical applications, such as nuclear magnetic resonance spectroscopy, radar target positioning, etc., the target signal we are interested in can be modeled as a linear superposition of several spectral peaks in the frequency domain (relative to the time domain), and the collected data is in the time domain ( Relative frequency domain) signal, and fits the exponential function. In actual sampling, usually due to limitations of hardware and physical conditions, in order to speed up sampling, etc., the actual sampling data is not complete or does not reach the expected resolution, and even only a very small part of it can be obtained. Data, it is necessary to complete the missing part of the collected data. Especially in the field of h...

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Problems solved by technology

The lengthy high-dimensional NMR experiment time not only makes the experiment consume a lot of spectrometer time, but also increases the difficulty of experimenting with unstable protein samples, thus limiting the application of high-dimensional NMR technology in protein research

In order to shorten the time of high-dimensional NMR experiments, a common practice is to use non-uniform sampling to reduce the number of sampling points in the time domain (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.) (Xiaobo Qu, Di Guo, Xue Cao, Shuhui Cai and Zhong Chen. Reconstruction of self-sparse 2D NMR spectrum from undersampled data in indirect dimension, Sensors, vol.11, no.9, pp.8888-8909, 2011.), but this will cause the signal to be lost, and the signal needs to be completed

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