19 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
Combined First- and Second-Order Variational Model for Image Compressive Sensing
A hybrid variational model combined first- and second-order total variation for image reconstruction from its finite number of noisy compressive samples is proposed in this paper. Inspired by majorization-minimization scheme, we develop an efficient algorithm to seek the optimal solution of the proposed model by successively minimizing a sequence of quadratic surrogate penalties. Both the nature and magnetic resonance (MR) images are used to compare its numerical performance with four state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm obtained a significant improvement over related state-of-the-art algorithms in terms of the reconstruction relative error (RE) and peak signal to noise ratio (PSNR)