Intelligent Design For Compressed Sensing Measurement Matrix And Reconstruction Algorithm

Compressed sensing theory is a new compress theory to reconstruct signals by solving nonlinear optimization problems.Current research topics includes sparse representation,measurement matrix design and reconstruction algorithm.In this thesis,we only focus the measurement matrix design and reconstruction algorithms.Firstly,measurement matrix is a crucial factor to influence the reconstruction accuracy,such as Gaussian matrix and Bernoulli matrix.However,both of them are randomly,and no any relation with problem.Therefore,a recent proposed population-based optimization algorithm,bat algorithm is employed to optimize the measurement matrix so that the problem knowledge can be added into this matrix.To further improve the performance,an adaptive bat algorithm is designed to increase the escaping probability from local optima.To test the validity,the orthogonal matching pursuit algorithm(OMP)is employed to reconstruct the original signals or images.When compared with Gaussian measure matrix method,the performance improvement rate for signal is larger than 19%,while for image,the PSNR improvement rate is no worse than 6.22%,and the SSIM improvement rate is 9.87%.Secondly,the traditional OMP does often find a local optimum.To improve the search accuracy,a discrete version of bat algorithm is designed to find the better order set of atomic.Furthermore,the measurement matrix is also optimized by adaptive bat algorithm.To test the validity,we compare our modification with OMP,the performance improvement rate of signal reconstruction error is larger than 24%,and PSNR improvement rate of the image is 16.81%,and SSIM improvement rate is no less than 20.87%.Finally,we propose a discrete multi-objective bat algorithm to optimize the measurement error and sparsity.In this algorithm,adaptive bat algorithm is used to optimized the measurement matrix,while knee-point and preference method are used to select the final result.Compared with OMP,the performance improvement rate of signal reconstruction error is larger than 24.00%,and the PSNR performance improvement rate of the image is no less than 16.21%,and the SSIM performance improvement rate is at least 20.7%.