Wavelet Methods for Inverting the Radon Transform with Noisy Data

Wavelet Methods for Inverting the Radon Transform with Noisy Data (2000)

by Nam-Yong Lee , Bradley J. Lucier

Venue:	IEEE TRANS. IMAGE PROC
Citations:	15 - 0 self

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Datum	Value	Source
TITLE	Wavelet Methods for Inverting the Radon Transform with Noisy Data	user correction - Legacy Corrections
AUTHOR NAME	Nam-Yong Lee	user correction
AUTHOR NAME	Bradley J. Lucier	user correction
ABSTRACT	Because the Radon transform is a smoothing transform, any noise in the Radon data becomes magnified when the inverse Radon transform is applied. Among the methods used to deal with this problem is the Wavelet-Vaguelette Decomposition (WVD) coupled with Wavelet Shrinkage, as introduced by David L. Donoho. We extend several results of Donoho and others here. First, we introduce a new sufficient condition on wavelets to generate a WVD. For a general homogeneous operator, which class includes the Radon transform, we show that a variant of Donoho's method for solving inverse problems can be derived as the exact minimizer of a variational problem that uses a Besov norm as the smoothing functional. We give a new proof of the rate of convergence of wavelet shrinkage that allows us to estimate rather sharply the best shrinkage parameter needed to recover an image from noise-corrupted data. We conduct tomographic reconstruction computations that support the hypothesis that near-optimal shrinkage pa...	user correction
YEAR	2000	user correction - Legacy Corrections
VENUE	IEEE TRANS. IMAGE PROC	user correction
VENUE TYPE	JOURNAL	INFERENCE
PAGES	79--94	INFERENCE
VOLUME	10	INFERENCE
CITATIONS	48 found	ParsCit 1.0