相关论文: Adaptive Anisotropic Total Variation - A Nonlinear…

We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…

The recently introduced second order total generalised variation functional $\mathrm{TGV}_{\beta,\alpha}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $\alpha$ and…

Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art…

Owing to its significant success, the prior imposed on gradient maps has consistently been a subject of great interest in the field of image processing. Total variation (TV), one of the most representative regularizers, is known for its…

Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…

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…

Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image, but they tend to blur the…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…

The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…

The spatio-spectral total variation (SSTV) model has been widely used as an effective regularization of hyperspectral images (HSI) for various applications such as mixed noise removal. However, since SSTV computes local spatial differences…

This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such problems we consider regularizers consisting of two terms that must be…

Although regularization methods based on derivatives are favored for their robustness and computational simplicity, research exploring higher-order derivatives remains limited. This scarcity can possibly be attributed to the appearance of…

Adaptive spectral (AS) decompositions associated with a piecewise constant function $u$ yield small subspaces where the characteristic functions comprising $u$ are well approximated. When combined with Newton-like optimization methods for…

The total generalized variation (TGV) is a popular regularizer in inverse problems and imaging combining discontinuous solutions and higher order smoothing. In particular, empirical observations suggest that its order two version strongly…

The paper is concerned with the inverse scattering problem for Maxwell's equations in three dimensional anisotropic periodic media. We study a new imaging functional for fast and stable reconstruction of the shape of anisotropic periodic…

We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised…

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…

A common strategy in variational image recovery is utilizing the nonlocal self-similarity (NSS) property, when designing energy functionals. One such contribution is nonlocal structure tensor total variation (NLSTV), which lies at the core…

In many image and signal processing applications, as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or color image restoration in HSV or LCh spaces the data has its range on the one-dimensional…