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Curvelets { A Surprisingly E®ective Nonadaptive Representation For Objects with Edges
Nonadaptive Representation Edges
2015/8/21
. It is widely believed that to e±ciently represent an otherwise
smooth object with discontinuities along edges, one must use an adaptive
representation that in some sense `tracks' the shape of the ...
Let C(t) : I 7! R2 be a simple closed unit-speed C2 curve in R2 with normal ~n(t). The
curve C generates a distribution ¡ which acts on vector ˉelds ~v(x1; x2) : R2 7! R2 by line
integration ac...
Curvelets and Wave Atoms for Mirror-Extended Images
Curvelets Wave Atoms Mirror-Extended Images
2015/7/15
We present variants of both the digital curvelet transform, and the digital wave atom transform, which handle the image boundaries by mirror extension. Previous versions of these transforms treated im...
Curvelets–A Surprisingly Effective Nonadaptive Representation For Objects with Edges
Curvelets Nonadaptive Representation Objects with Edges
2015/6/17
It is widely believed that to efficiently represent an otherwise smooth object with discontinuities along edges, one must use an adaptive representation that in some sense ‘tracks’ the shape of the di...
Let C(t) : I 7→ R2 be a simple closed unit-speed C2 curve in R2 with normal ~ n(t). The curve C generates a distribution Γ which acts on vector fields ~ v(x1,x2) : R2 7→ R2 by line integration accordi...
Curvelets and Reconstruction of Images from Noisy Radon Data
Ill-Posed Inverse Problems Regularization Singular Value Decomposition Radon Transform Deconvolution Edge Edge-Preserving Regularization Wavelet-Vaguelette-Decomposition
2015/6/17
The problem of recovering an input signal from noisy and linearly distorted data arises in many different areas of scientific investigation; e.g., noisy Radon inversion (tomography) is a problem of sp...
Curvelets,Multiresolution Representation, and Scaling Laws
Edges Partitioning Subband Filtering Local Fourier Transform Ridge functions Ridgelets Multiscale ridgelets Pyramids
2015/6/17
Curvelets provide a new multiresolution representation with several features that set them apart from existing representations such as wavelets, multiwavelets, steerable pyramids, and so on. They are ...
A recent body of work introduced new tight-frames of curvelets [3, 4] to address key problems in approximation theory and image processing. This paper shows that curvelets essentially provide optimall...
New Tight Frames of Curvelets and Optimal Representations of Objects with C2 Singularities
Curvelets wavelets second dyadic decomposition edges nonlinear approximation singularities thresholding Radon transform
2015/6/17
This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges.Conceptually, the curvelet transfo...