The received wave field including primaries and all of the multiples can be associated with the reflection coefficients which are only primaries by a prediction operator and two equations： the energy flux conservatio...The received wave field including primaries and all of the multiples can be associated with the reflection coefficients which are only primaries by a prediction operator and two equations： the energy flux conservation equation and the prediction operator equation that is developed from the Levinson recursion and can be easily solved by Li group method under a two-dimensional condition. Given reflection coefficients, the prediction operator can be obtained by solving the prediction operator equation. By the energy flux conservation equation, the reciprocal of the prediction operator times the conjugate of it, the wave field can be predicted, in which both of the surface multiples and the internal multiples are involved. On the other hand, if the wave field is given, based on the energy flux conservation equation solved by the 2D spectral factorization, a fully automated data-driven algorithm is developed to remove the surface multiples as well as the internal multiples.展开更多
The anisotropy of the land surface can be best described by the bidirectional reflectance distribution function (BRDF). As the field of multiangular remote sensing advances, it is increasingly probable that BRDF model...The anisotropy of the land surface can be best described by the bidirectional reflectance distribution function (BRDF). As the field of multiangular remote sensing advances, it is increasingly probable that BRDF models can be inverted to estimate the important biological or climatological parameters of the earth surface such as leaf area index and albedo. The state-of-the-art of BRDF is the use of the linear kernel-driven models, mathematically described as the linear combination of the isotropic kernel, volume scattering kernel and geometric optics kernel. The computational stability is characterized by the algebraic operator spectrum of the kernel-matrix and the observation errors. Therefore, the retrieval of the model coefficients is of great importance for computation of the land surface albedos. We first consider the smoothing solution method of the kernel-driven BRDF models for retrieval of land surface albedos. This is known as an ill-posed inverse problem. The ill-posedness arises from that the linear kernel driven BRDF model is usually underdetermined if there are too few looks or poor directional ranges, or the observations are highly dependent. For example, a single angular observation may lead to an under-determined system whose solution is infinite (the null space of the kernel operator contains nonzero vectors) or no solution (the rank of the coefficient matrix is not equal to the augmented matrix). Therefore, some smoothing or regularization technique should be applied to suppress the ill-posedness. So far, least squares error methods with a priori knowledge, QR decomposition method for inversion of the BRDF model and regularization theories for ill-posed inversion were developed. In this paper, we emphasize on imposing a priori information in different spaces. We first propose a gen-eral a priori imposed regularization model problem, and then address two forms of regularization scheme. The first one is a regularized singular value decomposition method, and then we propose a retrieval method in l1 space. We show that the proposed method is suitable for solving land surface parameter retrieval problem if the sampling data are poor. Numerical experiments are also given to show the efficiency of the proposed methods.展开更多
文摘The received wave field including primaries and all of the multiples can be associated with the reflection coefficients which are only primaries by a prediction operator and two equations： the energy flux conservation equation and the prediction operator equation that is developed from the Levinson recursion and can be easily solved by Li group method under a two-dimensional condition. Given reflection coefficients, the prediction operator can be obtained by solving the prediction operator equation. By the energy flux conservation equation, the reciprocal of the prediction operator times the conjugate of it, the wave field can be predicted, in which both of the surface multiples and the internal multiples are involved. On the other hand, if the wave field is given, based on the energy flux conservation equation solved by the 2D spectral factorization, a fully automated data-driven algorithm is developed to remove the surface multiples as well as the internal multiples.
基金This research was supported by the National Basic Research Program of China （Grant No. 2007CB209603）, Key Project of the National Natural Science Foundation （Grant No. 40830424）, State Key Laboratory of Geological Processes and Mineral Resources Geo-detection Laboratory of the Ministry of Education for their sponsorship （GPMR 200633, GDL0801）.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10501051, 10871191)Key Project of Chinese National Programs for Fundamental Research and Development (Grant Nos. 2007CB714400, 2005CB422104)
文摘The anisotropy of the land surface can be best described by the bidirectional reflectance distribution function (BRDF). As the field of multiangular remote sensing advances, it is increasingly probable that BRDF models can be inverted to estimate the important biological or climatological parameters of the earth surface such as leaf area index and albedo. The state-of-the-art of BRDF is the use of the linear kernel-driven models, mathematically described as the linear combination of the isotropic kernel, volume scattering kernel and geometric optics kernel. The computational stability is characterized by the algebraic operator spectrum of the kernel-matrix and the observation errors. Therefore, the retrieval of the model coefficients is of great importance for computation of the land surface albedos. We first consider the smoothing solution method of the kernel-driven BRDF models for retrieval of land surface albedos. This is known as an ill-posed inverse problem. The ill-posedness arises from that the linear kernel driven BRDF model is usually underdetermined if there are too few looks or poor directional ranges, or the observations are highly dependent. For example, a single angular observation may lead to an under-determined system whose solution is infinite (the null space of the kernel operator contains nonzero vectors) or no solution (the rank of the coefficient matrix is not equal to the augmented matrix). Therefore, some smoothing or regularization technique should be applied to suppress the ill-posedness. So far, least squares error methods with a priori knowledge, QR decomposition method for inversion of the BRDF model and regularization theories for ill-posed inversion were developed. In this paper, we emphasize on imposing a priori information in different spaces. We first propose a gen-eral a priori imposed regularization model problem, and then address two forms of regularization scheme. The first one is a regularized singular value decomposition method, and then we propose a retrieval method in l1 space. We show that the proposed method is suitable for solving land surface parameter retrieval problem if the sampling data are poor. Numerical experiments are also given to show the efficiency of the proposed methods.
