An image measurement matrix optimization method based on reconstruction errors

Abstract

The invention provides a measurement matrix optimization robustness method based on MSE. The method is based on a traditional model for optimizing a measurement matrix, a regular item is added and theregular item represents the mean square error of the original image and the reconstructed image. The method comprises the following steps of assuming that a mean square error obeys standard positivedistribution; carrying out the singular value decomposition by applying a center limit theorem and an equivalent dictionary, so that the optimization model of the measurement matrix is well simplified; finally using a gradient descent algorithm, so that the optimized measurement matrix is iteratively solved, the newly proposed image measurement matrix optimization model fully applies the information of the image, the cross correlation coefficient between the measurement matrix and the sparse base is reduced, the requirement on the sparsity is reduced, and the robustness of the image compressedsensing system is improved to a certain extent. Experiments show that independence between optimized measurement matrix columns is increased, and the reconstruction of high-quality image signals is facilitated.

Description

technical field [0001] The invention belongs to the field of signal processing, in particular to an image measurement matrix optimization method based on reconstruction error Background technique [0002] According to the Nyquist sampling theorem, it can be seen that the sampling frequency of the signal is required to be greater than or equal to twice the highest frequency of the signal to completely restore the original signal, which not only brings a huge pressure on the sampling rate of the hardware system, but also collects redundant information in Dalian, causing a large number of Waste of sampling resources. Compressed sensing (Compressive Sensing, CS) is a new theory proposed by Donoho, Candè et al. This theory breaks through the limitations of the traditional Nyquist sampling theorem, and realizes the acquisition and compression of image data at the same time, avoiding the The collection of a large amount of redundant information in images relieves the pressure on d...

AI Technical Summary

Problems solved by technology

This kind of method first obtains D=ΦΨ by the product of the measurement matrix Φ and the sparse dictionary Ψ, and constructs its corresponding Gram matrix. The off-diagonal elements of the matrix are the cross-correlation coefficients between the measurement matrix and the sparse dictionary. The characteristics of the matrix improve the performance of the measurement matrix. Elad uses the threshold method to reduce the off-diagonal elements of the Gram matrix, thereby reducing the correlation between the measurement matrix and the sparse dictionary. The simulation shows that the quality of the restored image is improved, but the algorithm parameter selection Relying on experience, the number of iterations is large, and the shrinking operation may introduce new interference; this algorithm is derived from the gradient descent method to make the Gram matrix approach the identity matrix, and gradually update it through the Equiangular Tight Frame (ETF) Gram matrix, let the off-diagonal elements of the Gram matrix matrix be equal to the maximum cross-correlation number of the matrix. Although the performance of image reconstruction is improved to a certain extent, there are still relatively large reconstruction errors between the original image and the restored image. In this paper, While optimizing the measurement matrix, the reconstruction error MSE of the sparse image signal is considered, and a robust algorithm for measurement matrix optimization based on MSE is proposed.

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