@article{discovery1518566,
       publisher = {IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC},
          volume = {26},
           month = {November},
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
           pages = {5176--5187},
         journal = {IEEE Transactions on Image Processing},
          number = {11},
            year = {2017},
           title = {Sparse Image Reconstruction on the Sphere: Analysis and Synthesis},
        keywords = {Harmonic analysis, Wavelet transforms, Manganese, Inverse problems, Image reconstruction, Dictionaries, sampling, spheres, rotation group, Wigner transform},
        abstract = {We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularization, exploiting sparsity in both axisymmetric and directional scale-discretized wavelet space. Denoising, in painting, and deconvolution problems and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the ?1 norm appearing in the regularization problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353-GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.},
             url = {http://dx.doi.org/10.1109/TIP.2017.2716824},
          author = {Wallis, CGR and Wiaux, Y and McEwen, JD},
            issn = {1941-0042}
}