Information-Theoretic Analysis For Compressive Sampling In Radar Imaging

Sparse microwave imaging is a proposed new concept in recent years, which aim-ing at improving present radar imaging structure and method by integrating sparse signal processing method like compressed sensing and traditional radar imaging theory. Radar compressive sensing, or compressed sensing based radar imaging, is the conjunc-tion and realization of compressed sensing theory with traditional radar imaging theory. Compressed sensing or CS (compressed sampling) is a signal measuring method using random projection, achieving the data compression in accordance with the signal acqui-sition when the sampling rate is far lower than the Nyquist rate, and the raw signal can be recovered through post-processing. As a new signal acquisition and processing method, compressed sensing is significant to radar application:the sub-nyquist sam-pling method in CS can reduce the sampling rate of the radar raw data, at the same time, CS reconstruction algorithm has potential substitution relative to classical signal processing algorithm.Within the area of study of compressed sensing, information theory has been im-portant research object and providing significant tools to study the performance limits of compressive sampling. As for the conditions of undersampling, the exsited methods are from combinotorial geometry or from information theory. But they are not suitable for being used in study the sampling ratio in radar imaging, as the measuring envi-ronment is different. Information theory is the branch of applied mathematics which utilizes probability theory and statistics to study communication, data transmission, compression and etc. As one of the basic theories for information engineering, informa-tion theory plays roles in evaluating the performace of imaging systems. For instance, the basic concept-mutual information-is important for radar waveform design, and pro-vide theoretic guild for study of radar resolution and the related information content. Besides, information theory also provides significant tools to study the performance limits of compressive sampling. Information theory has been studied in compressed sensing, but the results combining compressed sensing and radar imaging is rare, which contributes to the study aim of this paper.The main objective of this study is to research the compressed sensing problem in radar imaging environment under the theoretical framework of compressed sensing and information theory; specifically, build information theory models of compressed sensing problems in radar imaging and analyze radar imaging sample numbers in the condition of the reconstruction without distortion and distortion approximate reconstruction. The details of the research are listed below:(1) The basic concepts and theoretical basis of classical radar imaging and com-pressed sensing based radar imaging are interpreted. Composition and method of sig-nal processing of radar signal are described, the theory of classical radar imaging and compressed sensing are introduced, and the classical radar imaging algorithm and com-pressed sensing algorithm are explained.(2) The compressed sampling is derived from the expansion and extension of the classical sampling theorem, and the classical methods and information theory analysis method of compressed sampling conditions for traditional compressed sensing problems. It focus on the information theory analysis method of conventional compressed sampling conditions, including the source, channel, coding and other concepts; finally the sim-ulation experiment of radar imaging indicates the existing analysis method based on compressed sensing or information theory is limited for CS radar imaging research.(3) The conditions of sparse reconstruction without distortion of radar are ana-lyzed from the view of information theory. Focus on the compresses sampling process of transmitted signal and sparse imaging scene interaction, echo signal, from the per-spective of the information theory to analyze how to obtain the sparse imaging scene "information" through the forms of transmitting, receiving electromagnetic signals, and establish the source-radar channel model. For radar observation of sparse scene, sparse source model of radar scene and relative model parameters methods are provided at the first step; the amount of information with sparse scene itself can be computed, and then the ability of radar observation matrix information pass-through is quantitatively analyzed regarding the channel capacity as a tool; finally from the principle of undis-torted information reconstruction of compressed sampling, the conditions of realizing the undistorted scene reconstruction under radar compressed sampling are analyzed.(4) The sampling conditions for approximate reconstruction is studied with mutual information and rate distortion as tools, to study the relationships among undersam-pling ratio, SNR and scene sparsity. According to the information transmmision rule under restricted distortion, the neccessary undersampling ratios for CS-Radar imaging are derived and compared with phase diagrams based on computational methods, to prove the advantage of the information theoretic methods.The innovations of the thesis are:(1) A statistical modeling method based on Gaussian Mixture model for sparse radar scene with complex valued reflectivity, the in-phase and quadrature part are independtly modeled using the same GMM. From the experiment with real radar data, the GMM method is proved to be usedful.(2) A source-channel analysis method for radar compressed sampling based on GMM hypothesis. This method synthesis and expand the exsited computing method for information entropy and channel capacity. From analysis for conditions of under-sampling and signal reconstruction with non distortion, this method is proved to be practical.(3) A necessary sampling ratio determination method based on information content condition. From expanding the exsiting computing method of mutual information, the necessary sampling condition is derived from less information redundance principle. With compared to the exsiting sampling ratio analysis method, the method proposed is proved to more efficient.