Lanczos-based fast blind deconvolution methods (bibtex)
by Lara Dykes, Ronny Ramlau, Lothar Reichel, Kirk M. Soodhalter, Roland Wagner
Abstract:
The task of restoring an image that has been contaminated by blur and noise arises in many applications. When the blurring matrix (or equivalently, the point spread function) is explicitly known, this task commonly is referred to as deconvolution. In many applications only an approximation of the blurring matrix is available. The restoration task then is referred to as blind deconvolution. This paper describes a family of blind deconvolution methods that allow a user to adjust the blurring matrix used in the computation to achieve an improved restoration. The methods are inexpensive to use; the major computational effort required for large-scale problems is the partial reduction of an available large symmetric approximate blurring matrix by a few steps of the symmetric Lanczos process.
Reference:
Lanczos-based fast blind deconvolution methods (Lara Dykes, Ronny Ramlau, Lothar Reichel, Kirk M. Soodhalter, Roland Wagner), Technical report, Johann Radon Institute for Computation and Applied Mathematics, 2017.
Bibtex Entry:
@TECHREPORT{RRSW.2017,
  author = {Lara Dykes and Ronny Ramlau and Lothar Reichel and Kirk M. Soodhalter and Roland Wagner},
  title = {Lanczos-based fast blind deconvolution methods},
  institution = {Johann Radon Institute for Computation and Applied Mathematics},
  year = {2017},
  keywords = {paper},
  abstract = {The task of restoring an image that has been contaminated by blur and noise arises
in  many  applications.   When  the  blurring  matrix  (or  equivalently,  the  point  spread  function)  is
explicitly  known,  this  task  commonly  is  referred  to  as  deconvolution.   In  many  applications  only
an  approximation  of  the  blurring  matrix  is  available.   The  restoration  task  then  is  referred  to  as
blind  deconvolution.   This  paper  describes  a  family  of  blind  deconvolution  methods  that  allow  a
user to adjust the blurring matrix used in the computation to achieve an improved restoration.  The
methods are inexpensive to use; the major computational effort required for large-scale problems is
the partial reduction of an available large symmetric approximate blurring matrix by a few steps of
the symmetric Lanczos process.},
  number = {Report No. 2017-27},
  owner = {kirk},
  timestamp = {2017.09.12},
  url={https://www.ricam.oeaw.ac.at/files/reports/17/rep17-27.pdf}
}
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