544 research outputs found
Quaternion tensor ring decomposition and application for color image inpainting
In recent years, tensor networks have emerged as powerful tools for solving
large-scale optimization problems. One of the most promising tensor networks is
the tensor ring (TR) decomposition, which achieves circular dimensional
permutation invariance in the model through the utilization of the trace
operation and equitable treatment of the latent cores. On the other hand, more
recently, quaternions have gained significant attention and have been widely
utilized in color image processing tasks due to their effectiveness in encoding
color pixels. Therefore, in this paper, we propose the quaternion tensor ring
(QTR) decomposition, which inherits the powerful and generalized representation
abilities of the TR decomposition while leveraging the advantages of
quaternions for color pixel representation. In addition to providing the
definition of QTR decomposition and an algorithm for learning the QTR format,
this paper also proposes a low-rank quaternion tensor completion (LRQTC) model
and its algorithm for color image inpainting based on the QTR decomposition.
Finally, extensive experiments on color image inpainting demonstrate that the
proposed QTLRC method is highly competitive
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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