CS Reconstruction Algorithm Based On Gradient Optimization Research

Compressed sensing?CS?mainly consists of three steps,which are sparse,observation and reconstruction.The design of the reconstruction algorithm affects the effect of signal reconstruction.The greedy algorithm based on l₀ norm is an important class of reconstruction algorithms.In order to further improve the speed and accuracy of reconstruction,this paper combines the theory and method of gradient optimization to study the CS reconstruction algorithm:1.SL₀ algorithm is proposed based on PRP conjugate gradient.hyperbolic tangent function group is used to Approximate the l₀ norm,for the first time,through the PRP conjugate gradient method to solve the extreme function.The simulation results show that the mean square error of the algorithm is smaller than the reconstruction algorithm based on l₀ norm,and its performance is better.2.The gradient tracking algorithm based on L-BFGS research is proposed.The optimization Method of L-BFGS algorithm is combined with gradient tracking algorithm to update the direction of gradient tracking Method,and the gradient tracking algorithm based on L-BFGS is formed?L-BFGS Method based Gradient Pursuit,LMGP?.By comparing with other greedy algorithms,the proposed algorithm reconstruction in less time,better reconstruction result.3.an improved LMGP algorithm based on PRP conjugate gradient for dictionary learning is proposed.The sparse coefficient matrix is computed by the algorithm based on the PRP conjugate gradient algorithm in the sparse stage,and the original signal is represented by a sparse representation,so an improved LMGP algorithm based on PRP conjugate gradient for dictionary learning is proposed.Then,using the L-BFGS gradient tracking algorithm to reconstruct the video frame based on Simulation.The results show that the new algorithm in peak signal-to-noise ratio is superior to other algorithms,the algorithm has better performance.