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Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
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…
Hybrid-excited electrical machines aim to combine the advantages of permanent magnet machines (high efficiency and torque density) with those of separately excited machines (ease of flux-weakening at high speed). These machines are of…
The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…
Nowadays the deep learning technology is growing faster and shows dramatic performance in computer vision areas. However, it turns out a deep learning based model is highly vulnerable to some small perturbation called an adversarial attack.…
Purpose: Iterative Convolutional Neural Networks (CNNs) which resemble unrolled learned iterative schemes have shown to consistently deliver state-of-the-art results for image reconstruction problems across different imaging modalities.…
The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only…
Inpainting based image compression approaches, especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of…
In this paper, a two-grid method is proposed to linearize and symmetrize the steady-state Poisson-Nernst-Planck equations. The computational system is decoupled to linearize and symmetrize equations by using this method, which can improve…
In "extreme" computational imaging that collects extremely undersampled or noisy measurements, obtaining an accurate image within a reasonable computing time is challenging. Incorporating image mapping convolutional neural networks (CNN)…
Methods such as non-intrusive polynomial chaos (NIPC), and stochastic collocation are frequently used for uncertainty propagation problems. Particularly for low-dimensional problems, these methods often use a tensor-product grid for…
This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…
Interactive image restoration aims to generate restored images by adjusting a controlling coefficient which determines the restoration level. Previous works are restricted in modulating image with a single coefficient. However, real images…
In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use the multilevel correction method to transform the solution of eigenvalue problem to a series of solutions of the corresponding…
The color video inpainting problem is one of the most challenging problem in the modern imaging science. It aims to recover a color video from a small part of pixels that may contain noise. However, there are less of robust models that can…
Many real-world solutions for image restoration are learning-free and based on handcrafted image priors such as self-similarity. Recently, deep-learning methods that use training data have achieved state-of-the-art results in various image…
The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…
Progressive acquisition of slowly-scanned images is desirable for drift correction and real-time visualization. Interlacing methods are common approaches to storing and transmitting data on rectilinear grids, and here we propose using them…