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Journal Articles BIT Numerical Mathematics Year : 2018

Solution methods for linear discrete ill-posed problems for color image restoration

A. Bentbib
  • Function : Author
M. El Guide
  • Function : Author
E. Onunwor
  • Function : Author
Lothar Reichel

Abstract

This work discusses four algorithms for the solution of linear discrete ill-posed problems with several right-hand side vectors. These algorithms can be applied, for instance, to multi-channel image restoration when the image degradation model is described by a linear system of equations with multiple right-hand sides that are contaminated by errors. Two of the algorithms are block generalizations of the standard Golub–Kahan bidiagonalization method with the block size equal to the number of channels. One algorithm uses standard Golub–Kahan bidiagonalization without restarts for all right-hand sides. These schemes are compared to standard Golub–Kahan bidiagonalization applied to each right-hand side independently. Tikhonov regularization is used to avoid severe error propagation. Numerical examples illustrate the performance of these algorithms. Applications include the restoration of color images.
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Dates and versions

hal-04413581 , version 1 (23-01-2024)

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A. Bentbib, M. El Guide, Khalide Jbilou, E. Onunwor, Lothar Reichel. Solution methods for linear discrete ill-posed problems for color image restoration. BIT Numerical Mathematics, 2018, 58 (3), pp.555-576. ⟨10.1007/s10543-018-0706-0⟩. ⟨hal-04413581⟩
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