Study On Application Of Compressed Sensing Theory In Chirp Echoes Processing For Broadband Imaging Radar

With the support of a pre-researching project in"11th Five-Year-Plan"and a sub-project named"research of data acquisition and hardware implementation based on compressed sensing for imaging radar"in National Program on Key Basic Research Project of China (973 Program) named"research of theory, system and method for sparse microwave imaging", aiming at the huge cost of transmission, storage and imaging processing of broadband echoes caused by wideband direct sampling technology and large bandwidth in imaging radar, combining with the common Chirp signal model in radar and summarizing basic conclusion of compressed sensing theory, the following three main researching works have been developed in this dissertation: data compression for Chirp echoes, random selecting sampling for Chirp echoes and ISAR imaging processing of compressed Chirp echoes. Where, the compressed data is obtained from data compression or random selecting sampling.In the research on data compression for Chirp echoes, firstly, four redundant dictionaries are constructed with two approaches called machine learning and analysis. In the construction of redundant dictionary with machine learning approach, a sparse dictionary learning algorithm based on optimization of surrogate function is put forward and applied to the construction of redundant dictionary for Chirp echoes. The construction of redundant dictionary with analysis includes two aspects: one is to construct wave-form delay dictionary according to observing course of broadband radar and the other is to construct two time-frequency dictionaries (Gabor dictionary and Chirplet dictionary) according to time-frequency decomposition. The simulating result shows that all of the four dictionaries can be applied to sparse representation of Chirp echoes. Secondly, on the basis of construction of redundant dictionaries, reconstructable condition is analyzed combining with compressed sensing theory. The analyzing result indicates that the three dictionaries obtained with analysis approach satisfy the reconstructable condition. With three redundant dictionaries that satisfy the reconstructable condition, method of data compression for Chirp echoes is put forward and its validity is proved with simulation. Finally, aiming at the problem of large length of real-measured data, stagewise compression processing is put forward based on the method of data compression. The processing result of real-measured data indicates the validity of the stagewise compression processing and also indicates engineering feasibility of the method of data compression for Chirp echoes.In the research on randomly selecting sampling for Chirp echoes, firstly, the Stretch processing is reformulated in matrix form, and an orthogonal dictionary for sparse representation of Chirp echoes is constructed. This orthogonal dictionary is acquired easily and can be extended in other applications. Furthermore, influence on the orthogonal dictionary caused by high-speed movement of the target is unapparent. Secondly, on the basis of the orthogonal dictionary, the reconstructable condition for randomly selecting sampling is validated combined with the compressed sensing theory for sparse signal on orthogonal dictionary. Then the method and implementation flow for randomly selecting sampling is put forward. The method for randomly selecting sampling has been validated with simulation. In the end, in order to restrain reconstruction error caused by construction mode of the orthogonal dictionary, combined with the characteristic that the real data has huge length, stagewise overlap processing is introduced into the reconstruction for real data of Chirp echoes. Mathematical deduction analyzes the mechanism of stagewise overlap for restraining error. The processing result of the real data validates the effect of restraining error with stagewise overlap, and also indicates engineering feasibility of the method of randomly selecting sampling for Chirp echoes.In the research on ISAR imaging processing for compressed data of Chirp echoes, firstly, the principle of synthesizing frequency-stepped chirp signal into high resolution range profile is applied to Chirp echoes that are divided into many subsections with appropriate parameters. Then combined with the compressed sensing theory for sparse signal on orthogonal dictionary, the imaging method based on subsection randomly selecting for compressed data is put forward. The processing result of real-measured data indicates that the imaging method can evidently reduce the operating quantity of imaging process of compressed data and the imaging quality has no remarkable loss. Secondly, key idea of the imaging method based on subsection randomly selecting is applied to sampling of Chirp echoes and a mode of subsection randomly selecting sampling is obtained. In the end, continuity of distribution of scatterers in high resolution range profile is utilized and BOMP(Block Orthogonal Matching Pursuit) method is applied to reconstruct the high resolution range profile. The validity of BOMP in the reconstruction of high resolution range profile is proved with simulation. The processing result of the real-measured data indicates that BOMP method can improve the efficiency for reconstruction of high resolution range profile and the quality of reconstruction has no remarkable loss.