This is an interim version of our Electronic Legal Deposit Catalogue-eJournals and eBooks while we continue to recover from a cyber-attack.
An inner–outer iterative method for edge preservation in image restoration and reconstruction*SG's effort for this paper is supported in part by the EPSRC under Grants EP/P005985/1 and EP/T001593/1, and the NSF under Grant DMS-1906664. JGN's effort for this paper is supported in part by the US National Science Foundation under Grant DMS-1819042 and the NIH under Grant 1R13EB028700-01. ELM's effort for this paper is based upon work supported by the US Department of Homeland Security, Science and Technology Directorate, Office of University Programs, under Grant Award 2013-ST-061-ED0001 as well as NSF grants 1934553, 1935555, and 1720291. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the US Department of Homeland Security. (3rd December 2020)
Record Type:
Journal Article
Title:
An inner–outer iterative method for edge preservation in image restoration and reconstruction*SG's effort for this paper is supported in part by the EPSRC under Grants EP/P005985/1 and EP/T001593/1, and the NSF under Grant DMS-1906664. JGN's effort for this paper is supported in part by the US National Science Foundation under Grant DMS-1819042 and the NIH under Grant 1R13EB028700-01. ELM's effort for this paper is based upon work supported by the US Department of Homeland Security, Science and Technology Directorate, Office of University Programs, under Grant Award 2013-ST-061-ED0001 as well as NSF grants 1934553, 1935555, and 1720291. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the US Department of Homeland Security. (3rd December 2020)
Main Title:
An inner–outer iterative method for edge preservation in image restoration and reconstruction*SG's effort for this paper is supported in part by the EPSRC under Grants EP/P005985/1 and EP/T001593/1, and the NSF under Grant DMS-1906664. JGN's effort for this paper is supported in part by the US National Science Foundation under Grant DMS-1819042 and the NIH under Grant 1R13EB028700-01. ELM's effort for this paper is based upon work supported by the US Department of Homeland Security, Science and Technology Directorate, Office of University Programs, under Grant Award 2013-ST-061-ED0001 as well as NSF grants 1934553, 1935555, and 1720291. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the US Department of Homeland Security.
Abstract: We present a new inner–outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the two-norm and involves a regularization operator designed to improve edge resolution as the outer iterations progress, through an adaptive process. An efficient hybrid regularization method is used to project the Tikhonov-regularized problem onto approximation subspaces of increasing dimensions (inner iterations), while conveniently choosing the regularization parameter (by applying well-known techniques, such as the discrepancy principle or the L -curve criterion, to the projected problem). This procedure results in an automated algorithm for edge recovery that does not involve regularization parameter tuning by the user, nor repeated calls to sophisticated optimization algorithms, and is therefore particularly attractive from a computational point of view. A key to the success of the new algorithm is the design of the regularization operator through the use of an adaptive diagonal weighting matrix that effectively enforces smoothness only where needed. We demonstrate the value of our approach on applications in x-ray CT image reconstruction and in image deblurring, and show that it can be computationally much more attractive than other well-known strategies for edge preservation, while providing solutions of greater or equal quality.