Research On Methods For Resolution Enhancement Of SAR Image Based On Optimal Estimation

The resolution is an important index to measure and represent the quality of SAR images, and improving the resolution via the data processing techniques and parametric models is a significant way to remission the contradiction between the hardware levels of imaging systems and practice requirements for the resolution. At present, there are two valuable problems to be solved in the resolution enhancement field of SAR image: one is the incomplete resolution concept and mechanism of resolution enhancement, and the other is the non-adaptive solving process for related models induced by the unknown model parameters.This paper regards the resolution enhancement of SAR image as the estimation process of target parameters with high precision, and studies the above two problems based on the optimal estimation. The main contributions of this paper are listed as follows:(1) The connotation of resolution concept is extended and its dominating factors are investigated, which explain the resolution enhancement mechanismThe faults of the traditional resolution are analyzed and pointed out. Based on the Rayleigh criterion and the parametric model of two point targets, it investigates the effect of the coherence resulting from the different amplitudes and positions of targets on the traditional resolution. It comes to the conclusions that the two targets may be resolved even if the distance is smaller than the resolution. This fact conflicts with the Rayleigh criterion itself. Moreover, the existence of the highest measured resolution is proved using the cubic spline method, which means the nominal resolution is limited by the human vision system.The standard and model of extended resolutions in SAR image domain and frequency domain are proposed. To overcome these addressed faults, it utilizes the optimal estimation methodology, and proposes novel extended resolution concepts from the view of the hypothesis test and the estimation precision, based on the original resolution definition. Then, the compact and explicit expressions of the extended resolutions are obtained, which indicate the quantitative relationship between the resolution and the factors such as the noise level, signal power, etc. The obtained conclusions are coincident to the qualitative comprehension described in literatures and provide the explanation for existing resolution enhancement methods.(2)The criterion for selecting optimal model parameter is established, and the adaptive optimal solving processes are implementedThe direct solution of the generalized ridge estimation method in the complex domain is put forward. The ranges of iterative initial values are analyzed based on the bounded monotonous principle, and a binary equation set that the convergence solution must be satisfied is constructed. Then, the analytic solution is obtained, which avoids the time-consuming iterative process, implement the adaptive solving processing, and improve the estimation performance. By applying the similar process and minimum mean-square error criterion, the optimal model parameters and the analytic solution of the regularization model with l_k norm and identity matrix is also gotten. The comparison results of these two solutions shows that this regularization model is a special form of the generalized ridge estimation method when k→0~+.An adaptive optimal solving algorithm is proposed for the regularization model with l_k norm. A weighted regularization model with l_k norm is constructed based on the point target model. By analyzing the peculiarity of the iterative process and using the minimum mean-square error criterion, a matrix equation that the model parameters need to satisfy is constructed. Then, the suboptimal solution of it is obtained to design the adaptive iterative process, which establishes the relationship between model parameters, accurate values of target parameters and the noise level. Because it has not utilized the special property of the design matrix in the model, this method can be adopted directly to the generalized model such as the point enhancement model. Moreover, the superresolution imaging problem for multiple SAR images is studied preliminarily.A fast and adaptive method for basis selection is presented based on the character analysis of Fourier dictionary. According to the theoretical derivation and experimental verification in detail, the approximate orthogonality of the reconstructed (over-)complete Fourier dictionary is exploited. Then, a novel fast and adaptive method for basis selection is developed and the unbiased estimators of target parameters can be obtained easily by using the least-square method. This method belongs to the sequential basis selection strategy, but it is not a greedy algorithm and the selected basis does not be affected mutually. Moreover, it designs a calculation process based on the character of imaging parameters, which decreases the load of the computation and memory.