Research On Reconstruction Algorithms Of L_p-norm Regularization Problem In Compressed Sensing And Their Applications

Compressed sensing theory can accurately reconstruct the sparse signal under the premise of far lower Nyquist sampling rate,and the reconstruction algorithm is one of the core contents of the theory.In this paper,reconstruction algorithms of l_p-norm regularization problem in compressed sensing and their applications are researched,and the main work is as follows:To improve the reconstruction accuracy of the sparse signal,a smoothing conjugate gradient algorithm based on the Online Broyden-Fletcher-Goldfarb-Shanno(OBFGS)algorithm and the adaptive Barzilai-Borwein(BB)step size is proposed.In this algorithm,the OBFGS algorithm,which can approximate the Hessian inverse matrix of the objective function with higher accuracy,is used to improve the signal reconstruction accuracy.In addition,the algorithm uses the adaptive BB step size method to determine the step size of the OBFGS algorithm,which can ensure the accuracy of the algorithm and simplify the calculation of the step size.Numerical experimental results illustrate that compared with the smoothing strategy along with conjugate gradient algorithm before improvement and the classical half thresholding algorithm,our algorithm has higher reconstruction accuracy.The above improved algorithm is based on the approximation of the Hessian inverse matrix of the objective function for signal reconstruction.In order to further improve the reconstruction accuracy of the sparse signal,a smoothing Newton algorithm based on matrix dimension reduction and weighted function is proposed.Firstly,Newton method is used to calculate the Hessian inverse matrix to improve the signal reconstruction accuracy.Secondly,the matrix dimension reduction method is used to reduce the calculation amount of Newton method.Finally,the weighted function method is introduced to enhance the sparsity of the solution to further improve the signal reconstruction accuracy.Numerical experimental results illustrate that compared with the above improved algorithm and the fast iterative re-weighting algorithm based on sparse optimization l_p regularization,our algorithm has higher signal reconstruction accuracy.On the basis of the above algorithms,the two algorithms proposed in this paper are applied to study the reconstruction of computed tomography image.The experimental results of image reconstruction under different sampling rates show that compared with the fast iterative re-weighting algorithm based on sparse optimization l_p regularization,the proposed algorithms have better results in image reconstruction.