Related papers: Tensor Based Second Order Variational Model for Im…
We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the…
It is well-known that point sources with sufficient mutual distance can be reconstructed exactly from finitely many Fourier measurements by solving a convex optimization problem with Tikhonov-regularization (this property is sometimes…
Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated…
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…
Recently, tensor singular value decomposition (t-SVD) has emerged as a promising tool for hyperspectral image (HSI) processing. In the t-SVD, there are two key building blocks: (i) the low-rank enhanced transform and (ii) the accompanying…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship,…
Reconstructing objects with realistic materials from multi-view images is problematic, since it is highly ill-posed. Although the neural reconstruction approaches have exhibited impressive reconstruction ability, they are designed for…
Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to…
In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank $\star_{M}$-product format, whereby we aim to reconstruct an entire low-rank tensor from a small number of measurements…
Even though more than 30 years have passed since the seminal Rudin--Osher--Fatemi (ROF) paper on total variation (TV) denoising, it remains relevant, in particular in scientific applications such as astronomical imaging. However, it is…
Sampling from the posterior distribution poses a major computational challenge in solving inverse problems using latent diffusion models. Common methods rely on Tweedie's first-order moments, which are known to induce a quality-limiting…
In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace…
Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…
Recent work in CT imaging has seen increased interest in the use of total variation (TV) and related penalties to regularize problems involving reconstruction from undersampled or incomplete data. Superiorization is a recently proposed…
This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…
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…
The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a…
This paper proposes a homogeneous second-order descent framework (HSODF) for nonconvex and convex optimization based on the generalized homogeneous model (GHM). In comparison to the Newton steps, the GHM can be solved by extremal symmetric…