Variation Regularization Term Research Articles

Low-rank tensor singular value decomposition model for hyperspectral image super-resolution

We propose a method for hyperspectral image (HSI) super-resolution by designing a tensor singular value decomposition (t-SVD) and three-dimensional total variation (3D-TV) regularization terms. The super-resolution method is designed as an optimization problem whose cost function consists of a data-fidelity term, the low-rank representation term by t-SVD, and the 3D-TV regularization term. The sparse representation term is used to enhance the low-rank quality to unify the spectrum and space of HSI. Furthermore, the 3D-TV regularization term exploits the spectral and spatial similarity between adjacent pixels of HSI. Then we develop an effective algorithm for solving the resulting optimization by the alternative direction method of multipliers. The results on the simulated and the real data demonstrate that the proposed method is competitive with other state-of-the-art methods.

Notice of Violation of IEEE Publication Principles: Image Guided Depth Map Upsampling using Anisotropic TV- ${L^2}$

Notice of Violation of IEEE Publication Principles “Image Guided Depth Map Upsampling using Anisotropic TV-L2” by Xiaozhou Zhu, Xin Song, and Xiaoqian Chen in the IEEE Signal Processing Letters, Vol 22, Issue 3, March 2015, pp. 318-321 After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE's Publication Principles. This paper contains significant portions of text from the paper cited below that were reused without attribution. “Image Guided Depth Upsampling using Anisotropic Total Generalized Variation” by David Ferstl, Christian Reinbacher, Rene Ranftl, Matthias Ruether, and Horst Bischof in the Proceedings of the IEEE International Conference on Computer Vision, December 2013, pp. 993-1000 In this letter, we present a novel upsampling method to enhance the spatial resolution of depth maps. Given a low resolution depth map from a depth sensor and a registered high resolution intensity image from a camera, we formulate it as a convex optimization problem and solve it using the first-order primal-dual algorithm. The formulation combines an ${L^2}$ data term and an anisotropic total variation (TV) regularization term, thus it is more robust to noise and better preserves the fine details. Experimental results on Middlebury and real world datasets demonstrate that our method achieves favorable performance compared with state-of-the-art upsampling methods.

Image restoration with Poisson–Gaussian mixed noise

This study focuses on the image denoising and deconvolution problem in case of mixed Gaussian–Poisson noise. By using a maximum a posteriori estimator, we derive a new variational formulation whose minimisation provides the desired restored image. The new functional is composed of the total variation (TV) regularisation term, the Kullback–Leibler divergence term for Poisson noise and the norm fidelity term for Gaussian noise. We consider a dual formulation for the TV term, thus changing the minimisation into a minimax problem. A fast iterative algorithm is derived by using the proximal point method to compute the saddle point of the minimax problem. We show the capability of our model both on synthetic examples and on real images of low-count fluorescence microscopy.

A Narrow Band Method for the Convex Formulation of Discrete Multilabel Problems

We study a narrow band type algorithm to solve a discrete formulation of the convex relaxation of energy functionals with total variation regularization and nonconvex data terms. We prove that this algorithm converges to a local minimum of the original nonlinear optimization problem. We illustrate the algorithm with experiments for disparity computation in stereo and a multilabel segmentation problem, and we check experimentally that the energy of the local minimum is very near to the energy of the global minimum obtained without the narrow band type method.