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从模糊且含噪的观测中恢复凸边界AI 解读

We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set G. This approach is closely related to the method of…

霍夫变换估计量AI 解读

This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is to find the line that “best” fits a set of planar points. In particular, we establish strong consistency and rates of convergence, and characterize the limiting distribution of the Hough transform estimator. While the…

自回归时间序列建模的非渐近界AI 解读

The subject of this paper is autoregressive (AR) modeling of a stationary, Gaussian discrete time process, based on a finite sequence of observations. The process is assumed to admit an AR($\infty$) representation with exponentially decaying coefficients. We adopt the nonparametric minimax framework and study how well the process can be approximated by a finite­order AR model. A lower bound on the accuracy of AR approximations is derived, and a nonasymptotic upper bound on…