Research On SAR Image Reconstruction Based On Compressed Sensing

For a sparse or compressible signal,compressed sensing can compress the signal while sampling at a frequency much lower than the Nyquist sampling frequency,and a small number of observations can be used to reconstruct the data,overcoming the traditional high resolution Limitations of radar sampling.Under the theoretical framework of compressed sensing,SAR imaging greatly reduces the storage and processing time of radar data.This paper systematically analyzes the theoretical framework of compressed sensing from three aspects:sparse representation of signal,construction of measurement matrix,and reconstruction method of signal.It conducts in-depth research on traditional SAR image reconstruction algorithm,and based on SL0 algorithm and NSL0 algorithm In this paper,the fitting function and convergence problems adopted by the related methods are improved,and the UOSL0 and A-HNSL0 SAR image reconstruction methods in this paper are proposed.The main work of the full text is as follows:?1?The SL0 algorithm uses the steepest descent method in the iterative convergence process.This method is characterized by simple calculations and low initial iteration requirements.Although this method can quickly approach the optimal solution's close interval at the beginning of the iteration,it will appear“sawtooth”on the convergence path.The effect is more suitable for the first-stage process of solving the problem,and it is less efficient for the later-stage process.The NSL0 algorithm proposes to use the modified Newton method instead of the steepest descent method.Although it effectively solves the problem of"sawtooth"in the convergence path,the modified Newton method is more sensitive to the selection of the initial point of the iteration.The small value point is far away,and the iteration result may not converge or the convergence result is not ideal.Therefore,this paper proposes a UOSL0 SAR image reconstruction method based on the advantages and disadvantages of the steepest descent method and the modified Newton method.The basic idea of the UOSL0 reconstruction method is to use the steepest descent method to calculate at the initial stage of the iteration,find an initial point suitable for the modified Newton method,and then use the modified Newton method to iterate until the optimal solution is found.The experiment proves that the UOSL0 algorithm can effectively fuse the two iterative methods mentioned above and shorten the convergence time.?2?SL0 algorithm and NSL0 algorithm only use the error margin?as the end condition of the iteration during the solution process.This will cause the problem of iterating into an infinite loop when the value?is too small,and it will take too much time to get the desired result.Therefore,in this paper,an additional loop cutoff condition is added to the UOSL0 algorithm,that is,at each inner loop value is given a limited number?of times.In order to meet the error requirements after multiple iterations,the inner loop threshold will be triggered to end the inner loop under current?value.In this way,the phenomenon of infinite loop can be avoided.?3?In order to obtain a more accurate₀l norm approximate optimal solution,this paper introduces the approximate hyperbolic tangent function.Compared with the Gaussian function and the hyperbolic function,this function is more“steep”and has a higher degree of fitting to the₀l norm.Combining the approximate hyperbolic tangent function with the UOSL0 algorithm,an A-HNSL0 SAR image reconstruction method is proposed.The algorithm has good solution accuracy and fast convergence.From various experimental data analysis,it can be concluded that whether for high and low-dimensional data or different compression ratios,the peak signal to noise ratio,reconstruction error and reconstruction of the reconstructed image Performance indicators,such as time,have improved to some extent compared with the original algorithm.