A Wavelet Shrinkage Approach to Tomographic Image Reconstruction

A method is proposed for reconstructing images from tomographic data with respect to a two-dimensional wavelet basis. The Wavelet-Vaguelette Decomposition is used as a framework within which expressions for the necessary wavelet coe cients may be derived. These coe cients are calculated using a version of the ltered backprojection algorithm, as a computational tool, in a multiresolution fashion. The necessary lters are de ned in terms of the underlying wavelets. Denoising is accomplished through an adaptation of the Wavelet Shrinkage approach of Donoho et al., and amounts to a form of regularization. Combining the above two steps yields the proposed WVD/WS reconstruction algorithm, which is compared to the traditional ltered backprojection method in a small study.