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Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face…
We present a progressive image decomposition method based on a novel non-linear filter named Sub-window Variance filter. Our method is specifically designed for image detail enhancement purpose; this application requires extraction of image…
Uneven light image enhancement is a highly demanded task in many industrial image processing applications. Many existing enhancement methods using physical lighting models or deep-learning techniques often lead to unnatural results. This is…
We present adaptive finite difference ENO/WENO methods by adopting infinitely smooth radial basis functions (RBFs). This is a direct extension of the non-polynomial finite volume ENO/WENO method proposed by authors in \cite{GuoJung} to the…
Deep learning based techniques achieve state-of-the-art results in a wide range of image reconstruction tasks like compressed sensing. These methods almost always have hyperparameters, such as the weight coefficients that balance the…
Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some…
Including polynomials with small degree and stencil when designing very high order reconstructions is surely beneficial for their non oscillatory properties, but may bring loss of accuracy on smooth data unless special care is exerted. In…
Learned image reconstruction techniques using deep neural networks have recently gained popularity, and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect…
Spectral data is routinely broadened in order to improve appearance, approximate a higher sampling level or model experimental measurement effects. While there has been extensive work in the signal processing field to develop efficient…
This work is dedicated to the development and comparison of WENO-type reconstructions for hyperbolic systems of balance laws. We are particularly interested in high order shock capturing non-oscillatory schemes with uniform accuracy within…
In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-order hybrid fast sweeping scheme for solving steady state…
The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over…
Annotating lots of 3D medical images for training segmentation models is time-consuming. The goal of weakly supervised semantic segmentation is to train segmentation models without using any ground truth segmentation masks. Our work…
The decisive factor for the calculation accuracy of the mapped weighted essentially non-oscillatory scheme is the width of the center region of the mapping function. Through analysis of the classical mapped WENO schemes, the results show…
Motion estimation (ME) and motion compensation (MC) have been widely used for classical video frame interpolation systems over the past decades. Recently, a number of data-driven frame interpolation methods based on convolutional neural…
Third order WENO and CWENO reconstruction are widespread high order reconstruction techniques for numerical schemes for hyperbolic conservation and balance laws. In their definition, there appears a small positive parameter, usually called…
In this paper, we develop a simple, efficient, and fifth-order finite difference interpolation-based Hermite WENO (HWENO-I) scheme for one- and two-dimensional hyperbolic conservation laws. We directly interpolate the solution and…
In this paper we generalize to non-uniform grids of quad-tree type the Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput., 2001), thus obtaining a truly two-dimensional non-oscillatory third order reconstruction with…
We propose an unsupervised image segmentation approach, that combines a variational energy functional and deep convolutional neural networks. The variational part is based on a recent multichannel multiphase Chan-Vese model, which is…
We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…