Local inversion of the radon transform in the plane using wavelets

David Walnut

doi:10.1117/12.162090

1 November 1993 Local inversion of the radon transform in the plane using wavelets

David Walnut

Proceedings Volume 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing; (1993) https://doi.org/10.1117/12.162090
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform. These inversion formulas are local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error (epsilon) > 0, we can find (alpha) ((epsilon) ) > 0 such that this can be accomplished by knowing the projections of f only on lines passing through a ball of radius R + (alpha) ((epsilon) ) about x. We give explicit a priori estimates on the error in the L2 and L(infinity ) norms.

Citation Download Citation

David Walnut "Local inversion of the radon transform in the plane using wavelets", Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); https://doi.org/10.1117/12.162090

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