eprintid: 1518566
rev_number: 32
eprint_status: archive
userid: 608
dir: disk0/01/51/85/66
datestamp: 2016-10-02 03:08:22
lastmod: 2021-09-23 22:29:20
status_changed: 2017-12-05 14:51:09
type: article
metadata_visibility: show
creators_name: Wallis, CGR
creators_name: Wiaux, Y
creators_name: McEwen, JD
title: Sparse Image Reconstruction on the Sphere: Analysis and Synthesis
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F63
keywords: Harmonic analysis, Wavelet transforms, Manganese, Inverse problems, Image reconstruction, Dictionaries, sampling, spheres, rotation group, Wigner transform
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
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 ℓ1 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.
date: 2017-11
date_type: published
publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
official_url: http://dx.doi.org/10.1109/TIP.2017.2716824
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1145952
doi: 10.1109/TIP.2017.2716824
lyricists_name: McEwen, Jason
lyricists_name: Wallis, Christopher
lyricists_id: JMCEW60
lyricists_id: WALLI48
actors_name: Allington-Smith, Dominic
actors_id: DAALL44
actors_role: owner
full_text_status: public
publication: IEEE Transactions on Image Processing
volume: 26
number: 11
pagerange: 5176-5187
pages: 12
issn: 1941-0042
citation:        Wallis, CGR;    Wiaux, Y;    McEwen, JD;      (2017)    Sparse Image Reconstruction on the Sphere: Analysis and Synthesis.                   IEEE Transactions on Image Processing , 26  (11)   pp. 5176-5187.    10.1109/TIP.2017.2716824 <https://doi.org/10.1109/TIP.2017.2716824>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1518566/1/Wallis_1608.00553v2.pdf