Research On SAR Image Compressed Sensing Reconstruction Algorithm Based On Sparse Representation

The signal acquisition processing based on the traditional Nyquist sampling theory will produce a large amount of data when obtaining high-resolution radar images,which will bring great pressure to the hardware equipment.In recent years,compressed sensing,a new signal processing method based on sparse representation,has been proposed.Taking advantage of the sparse characteristic of signal,the samples of the signal can be obtained by compressed sensing in the condition of far less than the Nyquist sampling rate,and the signal can be reconstructed by using various nonlinear reconstruction algorithms.The technology does not need to collect too much redundant data,the imaging quality of synthetic aperture radar can be improved.The equipment and running costs of storage,transmission and processing can be greatly reduced.Therefore,it has a good application prospect.Based on the compressed sensing theory,the construction methods of sparse basis and the design of reconstruction algorithms are studied and analyzed comprehensively in this paper.The main research work of this paper is as follows:(1)The research situation of SAR image reconstruction at home and abroad is analyzed and summarized,the significance of SAR image reconstruction by using compressed sensing technology is briefly introduced.The basic concept and principle of compressed sensing,and three problems that need to be solved in compressed sensing reconstruction,including the sparse representation of signal,construction of measurement matrix and design of reconstruction algorithm are described in detail.(2)The first generation of Curvelet transform needs to be processed by subband division,smooth blocking,normalization,Ridgelet analysis and so on,among which the implementation of Ridgelet analysis is very complicated.The second generation of Curvelet transform is simpler and more efficient,which does not need Ridgelet analysis,but the transformed coefficients still contain a large amount of data.In order to solve the above-mentioned problems,a fast iterative contraction threshold algorithm is introduced in this paper.In order to further improve the accuracy and stability of the reconstruction algorithm,a positive definite weighted matrix is added on the basis of the fast iterative shrinkage threshold algorithm,and the objective function is transformed into a new minimization problem,which is then shrunk by the soft threshold function.Thus,a SAR image compression sensing reconstruction method based on discrete Curvelet transform is proposed..Experimental results show that the accuracy,stability and convergence speed of image reconstruction are improved by combining the improved fast iterative contraction threshold algorithm with the second-generation discrete Curvelet transform.(3)In the traditional SL0 reconstruction method,the NP-hard problem of solving the minimum l₀ norm is transformed into a convex optimization problem of solving the extreme value of the smoothing function by introducing the smoothing function.However,the SL₀reconstruction method uses the fastest descent method to search for the optimal solution,since the gradient descent direction of the two adjacent iteration points in the fastest descent method is orthogonal,the algorithm has a sawtooth effect,and the moving path of each iteration point in the algorithm presents a"Z"shape,which will affect the convergence speed of the algorithm.In order to solve the above-mentioned problems,a new SL0 reconstruction algorithm based on hybrid conjugate gradient is proposed.Based on the full study of FR,PRP and NPRP conjugate gradients,a new hybrid conjugate gradient is proposed to replace the traditional gradient descent method.The reconstruction experiments are carried out by using the Farmland,Lake and Harbor SAR images,which were obtained by different airborne SAR with different resolutions.The experimental results verify the effectiveness of the algorithm.Finally,the research work of this paper is summarized and prospected at the end of the paper.