Curvelets and reconstruction of images from noisy radon data

Emmanuel J. Candes; David L. Donoho

doi:10.1117/12.408569

4 December 2000 Curvelets and reconstruction of images from noisy radon data

Emmanuel J. Candes, David L. Donoho

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408569
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

The problem of recovering an input signal form noisy and linearly distorted data arises in many different areas of scientific investigation; e.g., noisy Radon inversion is a problem of special interest and considerable practical relevance in medical imaging. We will argue that traditional methods for solving inverse problems - damping of the singular value decomposition or cognate methods - behave poorly when the object to recover has edges. We apply a new system of representation, namely the curvelets in this setting. Curvelets provide near-optimal representations of otherwise smooth objects with discontinuities along smooth C² edges. Inspired by some recent work on nonlinear estimation, we construct a curvelet-based biorthogonal decomposition of the Radon operator and build a reconstruction based on the shrinkage of the noisy curvelet coefficients. This novel approach is shown to give a new theoretical understanding of the problem of edges in the Radon inversion problem.

Citation Download Citation

Emmanuel J. Candes and David L. Donoho "Curvelets and reconstruction of images from noisy radon data", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408569

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