A wavelet–vaguelet method for unfolding sphere size distributions
- 15 January 2002
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 18 (1) , 79-94
- https://doi.org/10.1088/0266-5611/18/1/306
Abstract
We consider the classical Wicksell problem of estimating an unknown probability density function of the radii of spheres in a medium, based on their observed random cross-sections. This problem is known as Wicksell's corpuscle problem. We first convert this problem to a form suitable for the application of thresholding vaguelet–wavelet methods for the solution of ill posed integral equations given noisy data. We outline the disadvantages of using standard kernel-type or cross-validated spline smoothing methods to solve this problem. A detailed description of the wavelet–vaguelet method applied to the Wicksell problem is given. The method relies upon a specifically built family of vaguelets.Keywords
This publication has 14 references indexed in Scilit:
- Wavelet decomposition approaches to statistical inverse problemsBiometrika, 1998
- Wavelet Threshold Estimators for Data with Correlated NoiseJournal of the Royal Statistical Society Series B: Statistical Methodology, 1997
- Wavelet-Galerkin methods for ill-posed problemsJIIP, 1996
- Stereological estimation of particle size distributionsAdvances in Applied Probability, 1995
- Estimating the Weight Undersize Distribution for the Wicksell problemStatistica Neerlandica, 1992
- The kernel method for unfolding sphere size distributionsJournal of Computational Physics, 1988
- A Statistical Perspective on Ill-Posed Inverse ProblemsStatistical Science, 1986
- Linear inverse problems with discrete data. I. General formulation and singular system analysisInverse Problems, 1985
- Cross-Validated Spline Methods for the Estimation of Three-Dimensional Tumor Size Distributions from Observations on Two-Dimensional Cross SectionsJournal of the American Statistical Association, 1984
- Thin-Section Mechanical Analysis of Indurated SedimentsThe Journal of Geology, 1935