TY - JOUR
T1 - Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ<sub>1</sub>-Constraints
AU - M. Tao
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 44
EP - 69
PY - 2018
DA - 2018/02
SN - 8
DO - http://doi.org/10.4208/eajam.210117.060817a
UR - https://global-sci.org/intro/article_detail/eajam/10884.html
KW - Parameter selection, $ℓ_1$-Constraints, alternating direction method of multipliers, impulsive noise, image processing.
AB - <p style="text-align: justify;">Minimisation of the total variation regularisation for linear operators under $ℓ_1$-constraints applied to image restoration is considered, and relationships between the
Lagrange multiplier for a constrained model and the regularisation parameter in an unconstrained
model are established. A constrained <span style="text-align: justify;">$ℓ_1$</span>-problem reformulated as a separable
convex problem is solved by the alternating direction method of multipliers that
includes two sequences, converging to a restored image and the “optimal&quot; regularisation
parameter. This allows blurry images to be recovered, with a simultaneous estimation
of the regularisation parameter. The noise level parameter is estimated, and numerical
experiments illustrate the efficiency of the new approach.</p>