针对统计非局部均值滤波损坏图像的细节与鲁棒性双边带滤波去噪不充分的缺点,提出了一种基于统计非局部均值滤波与鲁棒性双边带滤波相结合的复合滤波算法。该复合滤波算法通过统计非局部均值滤波与鲁棒性双边带滤波线性组合,利用Stein...针对统计非局部均值滤波损坏图像的细节与鲁棒性双边带滤波去噪不充分的缺点,提出了一种基于统计非局部均值滤波与鲁棒性双边带滤波相结合的复合滤波算法。该复合滤波算法通过统计非局部均值滤波与鲁棒性双边带滤波线性组合,利用Stein无偏风险估计对复合算法中的参数进行估计。实验中,从主观与客观方面进行对比分析,证明所提出的复合算法体现了非局部均值滤波与双边带滤波的优点,能有效地去除噪声并更好地保留图像的细节信息,峰值信噪比提高1-2 d B。展开更多
The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for thes...The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.展开更多
文摘针对统计非局部均值滤波损坏图像的细节与鲁棒性双边带滤波去噪不充分的缺点,提出了一种基于统计非局部均值滤波与鲁棒性双边带滤波相结合的复合滤波算法。该复合滤波算法通过统计非局部均值滤波与鲁棒性双边带滤波线性组合,利用Stein无偏风险估计对复合算法中的参数进行估计。实验中,从主观与客观方面进行对比分析,证明所提出的复合算法体现了非局部均值滤波与双边带滤波的优点,能有效地去除噪声并更好地保留图像的细节信息,峰值信噪比提高1-2 d B。
基金supported by National Science Foundation of USA (Grant No. DMS1265202)National Institutes of Health of USA (Grant No. 1-U54AI117924-01)
文摘The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.
