| Abstract: | 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 $u(x)∈\{f_1
,... , f_n\}$, $?x ∈ ?$. 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. |
