A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.
This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power ...This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.展开更多
In the medical computer tomography （CT） field, total variation （TV）, which is the l1-norm of the discrete gradient transform （DGT）, is widely used as regularization based on the compressive sensing （CS） theory...In the medical computer tomography （CT） field, total variation （TV）, which is the l1-norm of the discrete gradient transform （DGT）, is widely used as regularization based on the compressive sensing （CS） theory. To overcome the TV model＇s disadvantageous tendency of uniformly penalizing the image gradient and over smoothing the low-contrast structures, an iterative algorithm based on the l0-norm optimization of the DGT is proposed. In order to rise to the challenges introduced by the l0-norm DGT, the algorithm uses a pseudo-inverse transform of DGT and adapts an iterative hard thresholding （IHT） algorithm, whose convergence and effective efficiency have been theoretically proven. The simulation demonstrates our conclusions and indicates that the algorithm proposed in this paper can obviously improve the reconstruction quality.展开更多
To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l_0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l_0-norm co...To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l_0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l_0-norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent(DCD) iterations and the parallel processing to deal with the tapweight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steadystate behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer(DFE), the bite error rate(BER) decreases obviously.展开更多
Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a ...Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a modified relative total variation measure. In addition, the gradient constraint is adopted in objective function to eliminate the staircase effect, which can preserve the structure edges of small gradients. The experimental results show that compared with the state-of-the-art methods, especially the L0 gradient minimization method and the relative total variation method, the proposed method achieves better results in image texture smoothing and significant structure preserving.展开更多
Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground refl...Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.展开更多
基金This paper is a part of the author's series of letures at the Mathematical Institute of the Hungarian Academy of Sciences while visiting Hungary sent by the state Education Committee,the People's Republic of China.
文摘A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.
基金Supported by SSFC（04BTJ002）,the National Natural Science Foundation of China（10371016） and the Post-Doctorial Grant in Southeast University.
文摘This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.
文摘In the medical computer tomography （CT） field, total variation （TV）, which is the l1-norm of the discrete gradient transform （DGT）, is widely used as regularization based on the compressive sensing （CS） theory. To overcome the TV model＇s disadvantageous tendency of uniformly penalizing the image gradient and over smoothing the low-contrast structures, an iterative algorithm based on the l0-norm optimization of the DGT is proposed. In order to rise to the challenges introduced by the l0-norm DGT, the algorithm uses a pseudo-inverse transform of DGT and adapts an iterative hard thresholding （IHT） algorithm, whose convergence and effective efficiency have been theoretically proven. The simulation demonstrates our conclusions and indicates that the algorithm proposed in this paper can obviously improve the reconstruction quality.
基金supported by the National Natural Science Foundation of China (Grant No. 61471138, 50909029 and 61531012)Program of International S\&T Cooperation (Grant No. 2013DFR20050)+1 种基金the Defense Industrial Technology Development Program (Grant No. B2420132004)the Acoustic Science and Technology Laboratory (2014)
文摘To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l_0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l_0-norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent(DCD) iterations and the parallel processing to deal with the tapweight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steadystate behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer(DFE), the bite error rate(BER) decreases obviously.
基金Supported by the National Natural Science Foundation of China Youth Fund(No.61807029)Natural Science Foundation of Hebei Province(No.F2019203427).
文摘Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a modified relative total variation measure. In addition, the gradient constraint is adopted in objective function to eliminate the staircase effect, which can preserve the structure edges of small gradients. The experimental results show that compared with the state-of-the-art methods, especially the L0 gradient minimization method and the relative total variation method, the proposed method achieves better results in image texture smoothing and significant structure preserving.
基金supported by the National Natural Science Foundation of China(No.41422403)
文摘Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.
