Reduction of the Reconstruction Error With Lower and Upper Bounds in Synthetic Aperture Imaging Radiometers

Abstract

Synthetic aperture imaging radiometers (SAIRs) are powerful instruments for high-resolution Earth observation by use of small-aperture antennas sparsely arranged to achieve a large-aperture antenna. High-precision reconstruction algorithm is one of the key contents of SAIRs. Owing to the ill-posed problem and band-limited physical characteristic, there is a still large residual error for traditional regularization methods. It should be noted that the prior information like the lower and upper bounds of the brightness temperature distributions has not been utilized in the reconstruction procedure, especially for the open ocean with relatively small brightness temperature difference. In order to reduce the reconstruction error in SAIRs, a reconstruction method based on active set algorithm is presented by solving the least squares problems with lower and upper bounds. The simulation experiment results show that the proposed method can more effectively reduce the reconstruction error and better improve the accuracy of retrieved brightness temperature distributions in SAIRs than the band-limited regularization method, demonstrating the effectiveness of the proposed method.INDEX TERMS Imaging radiometry, synthetic aperture, inverse problem, reconstruction error.

Multi-Parameter Regularization Method for Synthetic Aperture Imaging Radiometers

“…However, it will have a high computational cost to directly estimate the optimal values of regularization parameters by minimizing Equation (12). In addition, the factorization method is not applicable to the minimization of the function (12).…”

“…However, it will have a high computational cost to directly estimate the optimal values of regularization parameters by minimizing Equation (12). In addition, the factorization method is not applicable to the minimization of the function (12). Therefore, in order to reduce the computational cost, the simplified multi-dimensional GCV method proposed previously [15] is used to choose multiple regularization parameters in the paper.…”

“…Therefore, in order to reduce the computational cost, the simplified multi-dimensional GCV method proposed previously [15] is used to choose multiple regularization parameters in the paper. The simplified method is based on the fact that the approximate stable solution can be obtained by minimizing the function X(α) = ( k ∑ i=1 w i (α i )) 2 instead of Equation (12). The specific process of the simplified method is that the i-th regularization parameter α i is estimated by minimizing the GCV criterion w i (α i ), and then the vector α = (α 1 ,•••,α k ) T is obtained by combining multiple regularization parameters.…”

“…Numerical regularization, such as truncated singular value decomposition (TSVD) and Tikhonov regularization [9], obtains a suitable solution by making use of mathematical methods to add the penalties. The active set method proposed previously [12] obtains a befitting solution by utilizing prior information of the open oceans like the lower and upper bounds of the brightness temperature distributions. However, there is still a large residual error on account of the ill-posed problem and band-limited physical characteristic [13].…”