Wavelet shrinkage in tomography

We use wavelet shrinkage methods to reconstruct images from tomographic data. Within the framework of Donoho's wavelet-vaguelette decomposition, we create a multiresolution analogue of the traditional filtering of backprojected projections approach to compute the empirical wavelet coefficients in an efficient manner. Level-dependent thresholds are used in shrinking these coefficients to accommodate the ill-posedness of the problem. Inversion of the result yields a denoised reconstruction of the underlying image with respect to a 2D wavelet basis.