1,077 research outputs found
Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization
We explore the use of the recently proposed "total nuclear variation" (TNV)
as a regularizer for reconstructing multi-channel, spectral CT images. This
convex penalty is a natural extension of the total variation (TV) to
vector-valued images and has the advantage of encouraging common edge locations
and a shared gradient direction among image channels. We show how it can be
incorporated into a general, data-constrained reconstruction framework and
derive update equations based on the first-order, primal-dual algorithm of
Chambolle and Pock. Early simulation studies based on the numerical XCAT
phantom indicate that the inter-channel coupling introduced by the TNV leads to
better preservation of image features at high levels of regularization,
compared to independent, channel-by-channel TV reconstructions.Comment: Submitted to Physics in Medicine and Biolog
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
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