Research On Some Problems In Compressed Sensing Based Radar Imaging

Compressive Sensing(CS) theory breaks through the classical Shannon-Nyquist sampling theory, indicating that sparse signal can be reconstructed exactly by far fewer samplings, and provids a new framework for signal aquisition. The reconstruction model of CS is a regularized least square problem, which can be solved by nonlinear methods. In radar imaging, CS has two advantages –on one side, it reduces the sampling ratio dramatically; on the other side, it has the potential of higher resolution than classical imaging methods.The content of this paper is focused on several problems in CS radar imaging. First, the development history of CS theory, its theory of foundations and the current situation of its application in radar imaging are introduced. Then the CS radar imaging model is established with stepped frequency signal. The reconstructing principle and processing procedure of SPGL1 recovery method are introduced in detail. Due to the signal process in CS radar imaging, in which the two dimensional radar image is taken as one dimensional signal, the sensing matrix is very large, taking so much memory and leading to the problem that the matrix-vector multiplication in recovery algorithms is very time-consuming. In this paper, two accelerating methods are proposed based on the Nonuniform Fast Fourier Transform for two different structures of matrix-vector multiplication. With the application of the two proposed methods, the computational complexity and holding memory of CS recovery algorithms are reduced dramatically.CS+BP imaging algorithm is introduced. We emphasize that the reason of breaking through Shannon-Nyquist Sampling Principle is due to its random sampling scheme, not the regularized least square model. Randomness is necessary for CS radar, otherwise, no advantage can be obtained in comparison to traditional imaging method. Due to complex operating environment, strong clutter is the primary problem for short range radar imaging. Traditional clutter reduction techniques are not suitable for non-fixed randomly chosen frequency sampling scheme. In this paper, classcial clutter reduction techniques are applied to fixed and non-fixed randomly chosen frequency sampling schemes. Combined with CS+BP imaging algorithm, real data are processed. From the imaging results, a conclusion can be obtained that, in nonfixed randomly chosen frequency samplig scheme, the method to abtain the uniform measurment data by CS and FFT is invalid; applying fixed randomly chosen frequency sampling scheme and being combined with traditional clutter reduction techniques and CS(or CS+BP) imaging algorithm is a valid method to supress the strong clutter for stationary target imaging in short range CS radar. Finally, based on CS+BP imaging algorithm in this sampling scheme, Through-the-Wall radar imaging with real data is completed and clear stationary targets image is obtained.Bayesian Compressive Sensing theory proposes a new explaination for compressive sensing from the perspective of probability and statistic theory. The sparsity of signal is described with a prior and the reconstruction is transformed into finding the Maximum A Posteriori estimate. Bayesian Compressive Sensing is deprived with real variables, while radar imaging data is complex. In this paper, two complex data extention models of Bayesian CS algorithm are deprived. The coresponding Fast Marginal Likelihood Maximization methods are deprived as well, and the reconstruction performance of the two methods is analysed. For the unknown noise parameter scenario, we propose a secondary reconstructing method, which can get good reconstruction result with proper estimation of noise parameter and improve the reconstruction performance without knowing the noise parameter. Simulation and real data imaging results demonstrate the validity of this method.