De-Noising By Soft-Thresholding-英文文献.pdf

DE-NOISING BY SOFT-THRESHOLDING David L. Donoho Department of Statistics Stanford University Abstract Donoho and Johnstone (1992a) prop osed a metho d for reconstruct- ing an unknown function f on [0 ; 1] from noisy data d = f (t ) +  z , i i i iid  ^ i = 0 ; : : : ; n 1, t = i=n , z  N (0 ; 1). The reconstruction f is i i n dened in the wavelet domain by translating all the empirical wavelet p p co ecients of d towards 0 by an amount 2 log(n )
 = n . We prove  ^ two results ab out that estimator. [Smo oth]: With high probability f n is at least as smo oth as f , in any of a wide variety of smo othness mea- sures. [Adapt]: The estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smo othness classes. These two prop erties are unprecedented in several ways. Our pro of of these results develops new facts ab out abstract statistical inference and its connection with