Compressed sampling sensing matrix disturbance optimization model construction method based on statistical learning

Abstract

The invention discloses a compressed sampling sensing matrix disturbance optimization model construction method based on statistical learning. The method comprises the following steps: setting a measurement matrix mathematical model phi with disturbance and a sparse matrix mathematical model psi with disturbance; obtaining a disturbance mathematical model A of the sensing matrix according to phi and psi, wherein the formula is A=[phi]*[psi]; obtaining a compressed sensing sparse signal model according to A, n being additive white Gaussian noise, theta being a sparse vector, and y being an observation data vector; and establishing a robust compressed sensing optimization function according to the sparse vector theta, and enabling f(theta) to be equal to ||theta||<1>, converting f(theta) into G (y0, y), and obtaining a sensing matrix disturbance optimization model. The statistical learning theory is applied to compressed sensing, and a robust compressed sensing reconstruction optimization mathematical model for resisting disturbance uncertainty in measurement is established, so that the influence of external environment and internal interference on the measurement uncertainty in thesampling process is reduced, and the accuracy of signal acquisition is improved.

Description

technical field [0001] The invention relates to the technical field of signal processing, in particular to a method for constructing a compression sampling sensor matrix disturbance optimization model based on statistical learning. Background technique [0002] At present, in the research of compressed sensing, more consideration is given to the assumption that the sparse signal is polluted by additive white Gaussian noise, but the measurement matrix and sparse matrix are subject to various external environments and internal interference during compressed sampling, which makes the actual obtained Both the measurement matrix and the sparse matrix are more or less added disturbances, which cause disturbances in the measurement and cause large deviations in the results, which have not been considered in depth. In practical application, the error of the measurement matrix in the measurement is often unavoidable, such as the error in the analog-to-digital conversion of the signal...

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Problems solved by technology

[0002] At present, in the research of compressed sensing, more consideration is given to the assumption that the sparse signal is polluted by additive white Gaussian noise, but the measurement matrix and sparse matrix are subject to various external environments and internal interference during compressed sampling, which makes the actual obtained Both the measurement matrix and the sparse matrix have more or less added disturbances, resulting in disturbances in the measurement, which in turn cause large deviations in the results, and have not been considered in depth.

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