Linear versus Non-Linear Acquisition of Step-Functions
نویسندگان
چکیده
منابع مشابه
Linear versus Non-linear Acquisition of Step-Functions
We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements? The stress is on a comparison of linear and nonlinear approaches. As a model case we use piecewise-constant functions on [0, 1], in particular, the Heaviside...
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We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements? The stress is on a comparison of linear and nonlinear approaches. As a model case we use piecewise-constant functions on [0, 1], in particular, the Heaviside...
متن کاملLinear versus Non-linear Approximation of Step-Functions
We investigate, from the point of view of a comparison of linear and non-linear approximation methods, one specific example, where many of important general phenomena become fairly apparent. This is the family of the step (or Heaviside) functions Ht(x), t ∈ [0, 1], defined for x ∈ [0, 1] by Ht(x) = 1, x ≤ t and Ht(x) = 0, x > t. The main problem we have in mind is compression of images, still a...
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2008
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-008-9016-0