Research On Sparsity-Driven Regularization Radar Imaging Theory And Method

Since radar imaging technique was proposed, its theoretic foundation has always been matched filtering. Matched filtering method is a linear process; it does not depend on any prior information of the targets, and has the advantages of simplicity and robustness to any scene. However, the drawbacks of matched filtering are also obvious. Since it does not use any prior information, it is difficult to break through its performance. The main drawback of the matched filtering is the requirement of sampling the signal according to the Shannon-Nyquist theorem, and the imaging resolution is also limited by the system bandwidth. That is to say, the matched filtering method has high requirements on the data but the performance of the result is limited. As radar imaging technique is developing fast, the performance objectives of radar imaging become higher and higher, and the matched filtering method will struggle to satisfy such requirements.In this thesis, radar imaging is analyzed through more generic mathematic models. Radar imaging can be considered as an inverse problem. It uses the measured electromagnetic wave scattering of the scene to conjecture the details of the scene. Due to the physical constraints, the information in the measured data is limited, such as limited bandwidth and limited observation angle. However, the pursuit of the details of the scene has no limits. So the expected information of the scene may more than the information in the measured data. Thus radar imaging is usually an ill-posed inverse problem. In this thesis, we argued that the classical least square estimation method can not solve the ill-posed inverse problem. The matched filtering method uses some approximations to the irreversible or unstable part in the least square estimate. The consequence of the approximation is that the result of the matched filtering has a main-lobe width and also has side-lobes. So the matched filtering method can only obtain an image with blurred details of the scene.The least square method also does not use any prior information, this cause it is unable to solve the ill-posed problem. Based on the least square method, the regularization method adds some constraint terms to make the ill-posed inverse problem can produce stable result. In order to make the obtained result accordant with the true value, the added constraint terms should based on the prior information of the scene. In this thesis, we also use the Bayesian maximum posterior probability(MAP) estimation theory to explain the regularization method. Regularization method and Bayesian estimation theory are both based on prior information, and they are coincident in essence.In radar imaging scenario, sparsity is the common prior information. This thesis focuses on the sparsity-driven regularization radar imaging method, and compressed sensing is a particular instance of the sparsity-driven regularization method. Since the sparse prior information is utilized, regularization(include compressed sensing) radar imaging method can improve the quality of the result and be robust in the case of a few measured data. This thesis investigate the issues of sparsity-driven regularization and(include compressed sensing) method when applied to radar imaging, include suitable waveform for sparse sampling, computational complexity of reconstruction, clutter problem, model error problem and sparse representation of extended scene.In waveform aspect, based on stepped frequency waveform, this thesis proposes a compressed sensing random frequency SAR imaging scheme. If the targets are sparse, according to the compressed sensing theory, the required number of frequencies can be significantly reduced, i.e. it is sufficient to transmit only a small number of random frequencies to exactly reconstruct the image of the targets. So that the limitations caused by traditional Shannon-Nyquist sampling theorem can be overcome. Compared to common used LFM waveform, the proposed method is more convenient for hardware implementation. Compared to stepped frequency waveform, compressed sensing random frequency SAR imaging scheme can significantly increase the imaging range width while maintain high resolution.In target reconstruction aspect, the computational complexity of conventional compressed sensing reconstruction process is quite huge. This thesis proposes a segmented reconstruction strategy. The basic thinking of the proposed method is splitting the whole scene into a set of sub-scenes; thereby achieve the aim of reducing the computational complexity. Since the radar data are the superposition of all echoes from the scene, it is unable to perform segmenting in the raw data domain. The steps of the proposed method are: reconstruct range profile using the radar data, split the range profile into sub-patches, reconstruct sub-scenes using the range profile sub-patches, and combine the sub-scenes into the whole scene. Compared to conventional compressed sensing reconstruction, the segmented reconstruction strategy can significantly reduce the computational complexity and the required memory, while the precision of the reconstruction are near the same.In clutter aspect, consider the characteristics of the clutter in sparse MIMO array forward-looking GPR imaging; this thesis proposes a clutter suppression pre-processing method and a regularization parameter determining method. In forward-looking GPR imaging, the targets of interest, such as landmines, are usually surrounded by ground surface clutter. In the proposed method, the azimuth clutter and near range clutter are suppressed before target reconstruction, in order to mitigate the influence of the clutter outside the reconstructed region. In the reconstruction process, it controls the target reconstruction ratio through the ratio of the unreconstructed clutter energy. The proposed method can exactly reconstruct sparse targets in clutter environment.In model error aspect, this thesis proposes a compressed sensing radar imaging method combined with observation position error estimation and compensation. The proposed method uses an iterative structure. In the first step of each iteration, the targets are reconstructed for a given observation model. In the second step, the observation position errors are then estimated using the reconstructed targets. Then the observation position error estimate is used to update the sensing matrix, and the algorithm passes to the next iteration. The target reconstruction step can be implemented using standard sparse reconstruction algorithms. The observation position error estimation step can be transformed into a set of unconstrained optimization problems. These problems can be solved effectively using gradient-based optimization algorithms. The proposed method can exactly reconstruct the targets while also exactly estimate the observation position error.In sparse representation aspect, consider that the phase of an extended scene is potential random, it may be unable to sparsely represent the complex-valued scene. This thesis proposes an improved magnitude sparsity-driven regularization radar imaging method. Based on the existing method, the proposed method uses more prior information; include the real-value information of the magnitude of the scene and the coefficient distribution prior information in the sparse representation. Since it uses more prior information, the proposed method has better reconstruction performance while requires lower computational complexity.