%P 5176-5187
%D 2017
%V 26
%A CGR Wallis
%A Y Wiaux
%A JD McEwen
%T Sparse Image Reconstruction on the Sphere: Analysis and Synthesis
%N 11
%X 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 â„“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.
%O This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
%I IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
%L discovery1518566
%J IEEE Transactions on Image Processing
%K Harmonic analysis, Wavelet transforms, Manganese, Inverse problems, Image reconstruction, Dictionaries, sampling, spheres, rotation group, Wigner transform