1,811 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
Fusing Multiple Multiband Images
We consider the problem of fusing an arbitrary number of multiband, i.e.,
panchromatic, multispectral, or hyperspectral, images belonging to the same
scene. We use the well-known forward observation and linear mixture models with
Gaussian perturbations to formulate the maximum-likelihood estimator of the
endmember abundance matrix of the fused image. We calculate the Fisher
information matrix for this estimator and examine the conditions for the
uniqueness of the estimator. We use a vector total-variation penalty term
together with nonnegativity and sum-to-one constraints on the endmember
abundances to regularize the derived maximum-likelihood estimation problem. The
regularization facilitates exploiting the prior knowledge that natural images
are mostly composed of piecewise smooth regions with limited abrupt changes,
i.e., edges, as well as coping with potential ill-posedness of the fusion
problem. We solve the resultant convex optimization problem using the
alternating direction method of multipliers. We utilize the circular
convolution theorem in conjunction with the fast Fourier transform to alleviate
the computational complexity of the proposed algorithm. Experiments with
multiband images constructed from real hyperspectral datasets reveal the
superior performance of the proposed algorithm in comparison with the
state-of-the-art algorithms, which need to be used in tandem to fuse more than
two multiband images
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