TY - JOUR
T1 - A Convex and Exact Approach to Discrete Constrained TV-L1 Image Approximation
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 172
EP - 186
PY - 2018
DA - 2018/02
SN - 1
DO - http://doi.org/10.4208/eajam.220310.181110a
UR - https://global-sci.org/intro/article_detail/eajam/10902.html
KW - Convex optimization, primal-dual approach, total-variation regularization, image processing.
AB - <p style="text-align: justify;">We study the TV-L1 image approximation model from primal and dual perspective,
based on a proposed equivalent convex formulations. More specifically, we
apply a convex TV-L1 based approach to globally solve the discrete constrained optimization
problem of image approximation, where the unknown image function $u(x)∈\{f_1
,... , f_n\}$, $∀x ∈ Ω$. We show that the TV-L1 formulation does provide an exact convex
relaxation model to the non-convex optimization problem considered. This result
greatly extends recent studies of Chan et al., from the simplest binary constrained case
to the general gray-value constrained case, through the proposed rounding scheme. In
addition, we construct a fast multiplier-based algorithm based on the proposed primal-dual
model, which properly avoids variability of the concerning TV-L1 energy function.
Numerical experiments validate the theoretical results and show that the proposed algorithm
is reliable and effective.</p>