From Local Polynomial Approximation to Pointwise Shape-adaptive Transforms: an Evolutionary Nonparametric Regression Perspective
نویسندگان
چکیده
In this paper we review and discuss some of the theoretical and practical aspects, the problems, and the considerations that pushed our research from the one-dimensional LPA-ICI (local polynomial approximation interesection of conÞdence intervals) algorithm [27] to the development of powerful transform-based methods for anisotropic image processing [18, 15, 19, 20, 8, 21]. In this paper we do not present a new algorithm. Instead, we propose a different and more general interpretation of our recently-developed image denoising algorithms. In particular, we show how they can be treated as nonparametric estimators based on aggregation of a family of local estimates which are pointwise-adaptive in terms of both shape and order.
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