The Study On The Reconstruction Technology Of Compressive Sensing

In the information era, researchers are challenged in how to obtain the necessary information from less data. Compressive sensing(CS) theory states that if a signal is sparse in time or some transform domain, it can be reconstructed from far fewer measurements than that required by the Shannon-Nyquist sampling theorem. The measurements of CS theory are from a random linear projection of the original signal, and the projection is realized by projecting the signal through a measurement matrix. Many researchers are concentrated on the design of compressive imaging(CI) systems that are designed based on CS theory, since CI systems can ease sensors’ burden of high sampling frequency. The present thesis first studies the improvement of CS reconstruction algorithm and the optimization method of measurement matrix. Because the quality assessment of the CS reconstructed images is an important method to evaluate the performance of reconstruction algorithm and measurement matrix, this thesis also studies the image quality assessment(IQA) method.The main contributions and innovations are listed as follows:A weighted spectral projected-gradient(WSPG) pursuit improvement method is proposed. WSPG uses Gaussian random variables as the weights, which are irrelevant to the unsolved signal. Utilizing the correlations between the signal’s neighour coefficients, this thesis uses the inverse of the mean of the absolute value of estimated coefficient’s neighbors as the weighted coefficient, and thus the improved WSPG algorithm is proposed. Experiments show that compared with WSPG algorithm, the modified one can improve the peak signal-to-noise ratio(PSNR) of the reconstructed images.The improvement methods of two-dimensional projected gradient(2DPG) pursuit are proposed in this thesis. 2DPG pursuit is a CS reconstruction algorithm proposed based on total variation regularization and Lagrangian method. The drawback of this algorithm is that when the minimization TV solution is estimated, the step value used in gradient descent method is determined manually, so the backtracking line search method, Barzilai-Borwein(BB) method, and nonmonotone projected BB method are used for the estimation of the step value in this thesis, respectively. The results of experiments show that the subjective IQA and the PSNR of the reconstructed images are both improved, when the improved methods are used.The optimized projection algorithm and the gradient-based alternating minimization measurement matrix optimization algorithm are optimized by eigenvalue decomposition and semi-QR factorization method. The optimized projection algorithm is proposed based on the theory of equiangular tight frame. Using eigenvalue decomposition method, the above zero eigenvalues of the Gram matrix of column normlization information operator are adjusted to be equal to each other, and thus the mutual coherence of information operator is decreased. Then semi-QR factorization method is used to improve the independency of the measurement matrix’s columns. The gradient-based alternating minimization measurement matrix optimization method is also improved using the same method. Results of experiments show that better image reconstruction results are obtained for both improved methods.An orthogonal measurement matrix optimization method is proposed based on incoherence principle of CS, which requires the mutual coherence of information operator to be small. The columns with mutual coherence are orthogonalized iteratively to decrease the mutual coherence of the information operator. An information operator with smaller mutual coherence is acquired after the optimization, leading to an improved measurement matrix in terms of its relationship with the information operator. Results of several experiments show that the improved measurement matrix can reduce its mutual coherence with dictionaries, compared with the random measurement matrix. The signal reconstruction error also decreases when the optimized measurement matrix is utilized.A no reference IQA(NR-IQA) method is proposed based on modulation transfer function(MTF). The blind/referenceless image spatial quality evaluator(BRISQUE) is a NR-IQA method proposed based on natural scene statistics(NSS), in which spatial features are used to do the IQA. Since MTF reflects the ability of an optical system to resolve a contrast at a given spatial frequency, the features of MTF are added to that of BRISQUE’s. Thus a NR-IQA method which has both spatial and frequency features is proposed for CS reconstructed images. The experimental results show that the proposed method is with higher correlation with differential mean opinion score(DMOS), compared with the results of BRISQUE algorithm.