Restrepo and Bovik : Locally Monotonic Regression
نویسنده
چکیده
The concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of a signal. The median filter is a suboptimal smoother under this measure of smoothness, since a filter pass does necessarily yield a locally monotonic output; even if a locally monotonic output does result, there is no guarantee that it will possess other desirable properties such as optimal similarity to the original signal. Locally monotonic regression is a technique for the optimal smoothing of finitelength discrete real signals under such a criterion. A theoretical framework where the existence of locally monotonic regressions is proven and algorithms for their computation are given. Regression is considered as an approximation problem in R", the criterion of approximation is derived from a semimetric and the approximating set is the collection of signals sharing the property of being locally monotonic.
منابع مشابه
Fast Digital Locally Monotonic Regression - Signal Processing, IEEE Transactions on
Locally monotonic regression is the optimal counterpart of iterated median filtering. In a previous paper, Restrepo and Bovik developed an elegant mathematical framework in which they studied locally monotonic regressions in R . The drawback is that the complexity of their algorithms is exponential in N . In this paper, we consider digital locally monotonic regressions, in which the output symb...
متن کاملOn the statistical optimality of locally monotonic regression
Aocally monotonic regression is a recently proposed technique for the deterministic smoothing of finite-length discrete signals under the smoothing criterion of local monotonicity. Locally monotonic regression falls within a general framework for the processing of signals that may be characterized in three ways: regressions are given by projections that are determined by semimetrics, the proces...
متن کامل2-D binary locally monotonic regression
We introduce binary locally monotonic regression as a first step in the study of the application of local monotonicity for image estimation. Given an algorithm that generates a similar locally monotonic image from a given image, we can specify both the scale of the image features retained and the image smoothness. In contrast to the median filter and to morphological filters, a locally monotoni...
متن کاملNonlinear image estimation using piecewise and local image models
We introduce a new approach to image estimation based on a flexible constraint framework that encapsulates meaningful structural image assumptions. Piecewise image models (PIMs) and local image models (LIMs) are defined and utilized to estimate noise-corrupted images, PIMs and LIMs are defined by image sets obeying certain piecewise or local image properties, such as piecewise linearity, or loc...
متن کامل