A method is proposed for reconstructing images from tomographic data with respect to a two-dimensional wavelet basis. The Wavelet-vaguelette decomposition (WVD) is used as a framework within which expressions for the necessary wavelet coefficients may be derived. These coefficients are calculated using a version of the filtered back-projection algorithm as a computational tool, in a multiresolution fashion. The necessary filters are defined in terms of the underlying wavelets. Denoising is accomplished through an adaptation of the wavelet shrinkage (WS) approach of Donoho et al. and amounts to a form of regularization. Combining these two steps yields the proposed WVD/WS reconstruction algorithm, which is compared to the traditional filtered backprojection method in a small study.