Recovering Edges in Ill-Posed Inverse Problems: Optimality of Curvelet Frames

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, that is, an edge. We use the continuum white-noise model, with noise level ε. Traditional linear methods for solving suc...

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Veröffentlicht in:	The Annals of statistics 2002-06, Vol.30 (3), p.784-842
Hauptverfasser:	Candès, Emmanuel J., Donoho, David L.
Format:	Artikel
Sprache:	eng
Schlagworte:	41A30 42C40 62C20 62G20 94A08 94A12 Applied sciences Approximations and expansions Coefficients curvelets Decision theory deconvolution Dyadics edge edge-preserving regularization Estimators Exact sciences and technology Fourier transformations Ill-posed inverse problems Information, signal and communications theory Inverse problems Mathematical analysis Mathematical functions Mathematics Minimax minimax estimation Nonparametric inference optimal rates of convergence Probability and statistics Radon Radon transform regularization ridgelets Sciences and techniques of general use Signal and communications theory Signal representation. Spectral analysis Signal, noise singular value decomposition Statistics Telecommunications and information theory Threshing wavelet shrinkage wavelet-vaguelette decomposition wavelets White noise white-noise model
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