Bayesian Spatially Varying Multi-Regularization Image Deblurring

Journal Article · Wed Dec 01 04:00:00 EST 2021 · Inverse Problems in Science and Engineering - https://www.tandfonline.com/journals/gipe20

OSTI ID:1835841

Pillow, Jordan A ^[1]; Howard, Marylesa M ^[1]; Adams, Jesse J ^[1]; Morzfeld, Matthias ^[2]; Kupinski, Matthew ^[3]

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1. Mission Support and Test Services, LLC (MSTS), North Las Vegas, NV (United States)
2. Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, CA, USA
3. Department of Optical Sciences, The University of Arizona, Tucson, AZ, USA

Many scientific experiments such as those found in astronomy, geology, microbiology, and X-ray radiography require the use of high-energy instruments to capture images. Since blur and noise are inevitably present in any imaging system, the images must be \deblurred" to extract the full information content. Mathematically, image deblurring is an ill-posed inverse problem that requires regularization. The regularization, in turn, has a large effect on the deblurred image: different regularization strengths, and types, lead to drastically different reconstructions. Moreover, many images contain a mixture of smooth and sharp features which suggests the use of multi-regularization, i.e., varying the type of regularization (e.g. Tikhonov or total variation) across the image. We address these issues by formulating the image deblurring problem within a hierarchical Bayesian framework in which we spatially adapt the strength of the regularization and also vary the regularization type across the image. In this way, the image itself, along with corresponding regularization strength at each pixel, are described jointly by a posterior distribution which we can sample by Markov chain Monte Carlo (MCMC) methods. We illustrate our techniques on simplified test problems and apply them to high-energy X-ray images taken at the Nevada National Security Site. Numerical tests show that our new method is robustly applicable and increases the quality of the image reconstruction when compared to other (Bayesian) methods.

• Research Organization: Nevada National Security Site/Mission Support and Test Services LLC, Las Vegas, NV (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
• DOE Contract Number: NA0003624
• OSTI ID: 1835841
• Report Number(s): DOE/NV/03624--1256; STIP WF - 27009247
• Journal Information: Inverse Problems in Science and Engineering - https://www.tandfonline.com/journals/gipe20, Journal Name: Inverse Problems in Science and Engineering - https://www.tandfonline.com/journals/gipe20
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Gibbs
bayesian
deblur
imaging
regularization