15,766 research outputs found
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
Generalized Forward-Backward Splitting with Penalization for Monotone Inclusion Problems
We introduce a generalized forward-backward splitting method with penalty
term for solving monotone inclusion problems involving the sum of a finite
number of maximally monotone operators and the normal cone to the nonempty set
of zeros of another maximal monotone operator. We show weak ergodic convergence
of the generated sequence of iterates to a solution of the considered monotone
inclusion problem, provided the condition corresponded to the Fitzpatrick
function of the operator describing the set of the normal cone is fulfilled.
Under strong monotonicity of an operator, we show strong convergence of the
iterates. Furthermore, we utilize the proposed method for minimizing a
large-scale hierarchical minimization problem concerning the sum of
differentiable and nondifferentiable convex functions subject to the set of
minima of another differentiable convex function. We illustrate the
functionality of the method through numerical experiments addressing
constrained elastic net and generalized Heron location problems
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