Research On Compressed Sensing Radar Imaging Under Model Mismatch

Traditional radar imaging methods depends on the Shannon-Nyquist sampling theorem.With the increasing bandwidth of modern radar system,the burden on data acquisition,storage and transmission are more and more heavy.The compressed sensing(CS)theory shows that a sparse signal can be reconstructed through convex optimization with far less non-adaptively sampled data than traditional methods use.Since the backscattering signal of wideband radar target can be depicted by a few number of scattering centers,thus the requirement of sparsity on target is satisfied which pave the way for utilizing the theory and method of CS to significantly reduce the number of measurements for imaging thus the high stress of signal sampling and transmitting on data acquisition device can be alleviated efficiently.Taking the high resolution wideband radar imaging under the far field assumption as application background,the dissertation is dedicated to deal with the problems of basis mismatch and large scale dictionary existed in the current CS based imaging approaches.Chapter 1 introduces the background and significance of the researches in this dissertation.The basic theory and algorithm of CS with its application in radar imaging are comprehensively reviewed.Then,the problems with the existing CS based imaging approach are discussed.Chapter 2 describes the basic principle of radar imaging based on CS which serves as a theoretical and algorithmic basis for the researches in the following Chapters.Firstly,the signal model and recovery guarantee are presented from a mathematical view,then the sparse recovery algorithms based on convex optimization and Bayesian method are.introduced in detail.After that,the models for one,two and three dimensional radar imaging and the model for CS based radar imaging are derived.Finally,the basis mismatch effect is verified by numerical simulations and the problem of large scale dictionary is analyzed.Chapter 3 studies the imaging approach based on the continuous compressed sensing(CCS)to address the basis mismatch problem.The CCS can establish its sparse representation model and conduct the sparse recovery directly in the continuous-valued parameter space without any basis mismatch.To reduce the complexity of solving the CCS problem,a more efficient first-order algorithm based on the alternating direction method of multipliers(ADMM)is developed which has been further accelerated by exploiting the low rank property of its sub-problem.In order to utilize the dual polynomial method to estimate the location of target,a method which can obtain the dual optimal solution from the primal solution of multiplier is proposed and proved based on the semidefinite programming(SDP)of primal and dual problems.The experimental results based on simulated and real data show that the reconstruction accuracy of the CCS is higher than the conventional discretization based CS approach.Moreover,the estimation accuracy of the dual polynomial method can achieve the Crammer-Rao lower bound(CRLB)and its ability of high-resolution radar imaging is comparable to that of traditional parametric spectral estimator.Chapter 4 proposes the approach based on the perturbation dictionary to address the problems of basis mismatch and larger scale dictionary.By applying first order Taylor approximation to the precise dictionary on both the pre-specified equally spaced wavenumber and target grid,a perturbation dictionary which has the form of two-dimensional(2-D)DFT matrix is established and exploited in the sparse recovery based on the sparse variational Bayesian inference algorithm.In the meanwhile,another approach which only applies the first order approximation to the precise dictionary on the pre-specified wavenumber grid and adopts a finer target grid is also proposed.to establish its 2-D DFT type perturbation dictionary.For this approach,the SPGL1 is adopted for sparse recovery based on the ?1 norm inimization.The experimental results based on simulated and real data show that they both can handle the problems of basis mismatch and large scale dictionary efficiently.By comparison,the second approach that uses a more simple perturbation based dictionary is less sensitive to the density of the pre-specified wavenumber and target grid,and has the advantages of higher reconstruction accuracy and computational efficiency.Chapter 5 studies the approach based on the perturbation dictionary for three dimensional compressed sensing radar imaging.On the basis of the conclusions of the Chapter 4,in this Chapter,the ?1 norm minimization method based on the perturbation dictionary is extended and applied to the problem of three dimensional radar imaging under compressed sensing.In the meantime,we also introduce the imaging approach based on tensor compressed sensing and improve its sampling scheme to allow completely random under-sampling.Experiments based on simulated and real data are conducted to test and compare the performance of the two algorithms.The experimental results demonstrate that the approach based on the perturbation dictionary and the approach based on tensor compressed sensing both have the capability to deal with the the problems of basis mismatch and large scale dictionary.By comparison,the competitive advantage of the perturbation dictionary based approach rests on a more accurate sparse representation model which makes it applicable to the compressed sensing radar imaging under the wide-angle observations.Chapter 6 concludes this dissertation,and gives some suggestions for future work.