The adaptive weights smoothing (AWS) procedure was introduced in Polzehl and Spokoiny (2000) in the context of image denoising. The procedure has some remarkable properties like preservation of edges and contrast, and (in some sense) optimal reduction of noise. The procedure is also fully adaptive and dimension free. Simulations with artificial images show that AWS is superior to classical smoo...

Functional linear models are useful in longitudinal data analysis. They include many classical and recently proposed statistical models for longitudinal data and other functional data. Recently, smoothing spline and kernel methods have been proposed for estimating their coe cient functions nonparametrically but these methods are either intensive in computation or ine cient in performance. To ov...

In this paper, a primal-dual algorithm for TV-type image restoration is analyzed and tested. Analytically it turns out that employing a global L-regularization, with s > 1, in the dual problem results in a local smoothing of the TV-regularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the `r-norm, with r−1 + s−1 = 1, and a smo...

In this paper, we develop a novel homotopy smoothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration complexity for solving such non-smooth optimization problems is O(1/ ) without any assumption on the...

Noise filtering of images is basically a smoothing process, and it is a subject that has been addressed for many years. The idea of adaptive smoothing is being investigated a long time and many different approaches have been proposed over the years. Mastin (1985) reported superior performance of nonlinear such as medina filtering over linear techniques applied for adaptive image smoothing. Zuck...

In this paper, we develop a novel homotopy smoothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration complexity for solving such non-smooth optimization problems is O(1/ ) without any assumption on the...

The pointwise traversal of a given path is a popular task in the area of robotics, e.g. in mobile, industrial or surgical robotics. The easiest method to describe paths is by a sequence of linear segments, and for many tasks the precision of a path approximated by linear segments is sufficient. The movements to be accomplished by a mobile robot or the robot’s end-effector are described by a seq...

Edge-aware smoothing is an essential tool for computer vision, graphics and photography. In this paper, we develop a new efficient local weighted average filter edge-aware smoothing. The proposed can use guidance information which permits iterative filtering process. Since the weights of depend on variance, implementation requires linear filters only, leading to $\mathcal {O}(N_{pix})$ computat...

We present a new optimization-theoretic approach to analyzing Follow-the-Leader style algorithms, particularly in the setting where perturbations are used as a tool for regularization. We show that adding a strongly convex penalty function to the decision rule and adding stochastic perturbations to data correspond to deterministic and stochastic smoothing operations, respectively. We establish ...