Wavelet-Based Multiresolution Local Tomography

Abstract

The reconstruction of a wavelet transform of an image directly from the Radon transform of the image has been of great interest recently [1-15]. Some applications of this technique include but are not limited to image enhancement, feature extraction directly from the Radon transform domain, and local tomography. The purpose of this chapter is to present methods of extracting wavelet transform coefficients directly from the Radon transform data and to show that wavelet transform methods are useful tools in the study of local and semilocal tomography. We also show that the various image analysis methods that employ wavelet transforms or other multiscale analyses intertwine with Radon transform inversion. This allows for the possibility of performing image enhancement or feature extraction directly on tomographic data.