Superresolution via sparsity constraints
SIAM Journal on Mathematical Analysis
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
SAR Image Superresolution via 2-D Adaptive Extrapolation
Multidimensional Systems and Signal Processing
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
On the use of a priori information for sparse signal approximations
IEEE Transactions on Signal Processing
Sparse representations in unions of bases
IEEE Transactions on Information Theory
Why Simple Shrinkage Is Still Relevant for Redundant Representations?
IEEE Transactions on Information Theory
SAR imaging via modern 2-D spectral estimation methods
IEEE Transactions on Image Processing
Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization
IEEE Transactions on Image Processing
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A novel fast and adaptive method for synthetic aperture radar (SAR) superresolution imaging is developed. Based on the point scattering model in the phase history domain, a dictionary is constructed so that the superresolution imaging process can be converted to a problem of sparse parameter estimation. The approximate orthogonality of this dictionary is exploited by theoretical derivation and experimental verification. Based on the orthogonality of the dictionary, we propose a fast algorithm for basis selection. Meanwhile, a threshold for obtaining the number and positions of the scattering centers is determined automatically from the inner product curves of the bases and observed data. Furthermore, the sensitivity of the threshold on estimation performance is analyzed. To reduce the burden of mass calculation and memory, a simplified superresolution imaging process is designed according to the characteristics of the imaging parameters. The experimental results of the simulated images and an MSTAR image illustrate the validity of this method and its robustness in the case of the high noise level. Compared with the traditional regularization method with the sparsity constraint, our proposed method suffers less computation complexity and has better adaptability.