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Monoscale Ridgelets for the Representation of Images with Edges
Edges Partitioning Local Fourier Transform (JPEG) Ridge functions Ridgelets Radon transform Nonlinear approximation
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2015/6/17
In a previous paper [1], the author introduced a new system for representing multivariate functions, namely, the ridgelets. In a following article [3], ridgelets were shown to be optimal for represent...
Curvelets–A Surprisingly Effective Nonadaptive Representation For Objects with Edges
Curvelets Nonadaptive Representation Objects with Edges
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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...
Ridgelets and Their Derivatives:Representation of Images with Edges
Ridgelets Derivatives Images with Edges
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2015/6/17
This paper reviews the development of several recent tools from computational harmonic analysis. These new systems are presented under a coherent perspective, namely, the representation of bivariate f...
Recovering Edges in Ill-Posed Inverse Problems:Optimality of Curvelet Frames
Ill-Posed Inverse Problems Regularization Singular Value Decomposition Radon Transform Deconvolution Edge Edge-Preserving Regularization Wavelets Curvelets Ridgelets Wavelet-Vaguelette-Decomposition Wavelet Shrinkage Minimax Estimation Optimal Rates of Convergence White Noise Model
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2015/6/17
We consider a model problem of recovering a function f(x1, x2) from noisy Radon data. The function f to be recovered is assumed smooth apart from a discontinuity along a C2 curve – i.e. an edge. We us...