Sparse Image Reconstruction on the Sphere: Analysis and Synthesis

作者：Wallis Christopher G R^*; Wiaux Yves; McEwen Jason D

来源：IEEE Transactions on Image Processing, 2017, 26(11): 5176-5187.

DOI：10.1109/TIP.2017.2716824

• Harmonic analysis
• sampling
• spheres
• rotation group
• Wigner transform

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, inpainting, 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 l(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.

• 出版日期2017-11