Related papers: Graph Laplacian assisted regularization method und…
We present a data-assisted iterative regularization method for solving ill-posed inverse problems. The proposed approach, termed \texttt{IRMGL+\(\Psi\)}, integrates classical iterative techniques with a data-driven regularization term…
We investigate a variational method for ill-posed problems, named $\texttt{graphLa+}\Psi$, which embeds a graph Laplacian operator in the regularization term. The novelty of this method lies in constructing the graph Laplacian based on a…
This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph…
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be obtained via replacing the Laplacian regulariser with a…
Image deblurring is relevant in many fields of science and engineering. To solve this problem, many different approaches have been proposed and among the various methods, variational ones are extremely popular. These approaches are…
We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic…
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…
Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
Recommendation algorithm plays an important role in recommendation system (RS), which predicts users' interests and preferences for some given items based on their known information. Recently, a recommendation algorithm based on the graph…
Semi-supervised Laplacian regularization, a standard graph-based approach for learning from both labelled and unlabelled data, was recently demonstrated to have an insignificant high dimensional learning efficiency with respect to…
Scalings in which the graph Laplacian approaches a differential operator in the large graph limit are used to develop understanding of a number of algorithms for semi-supervised learning; in particular the extension, to this graph setting,…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…
This paper presents a novel L1-norm semi-supervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm…
Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…
We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…
Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…
Low-dose computed tomography (LDCT) reconstruction faces a critical tradeoff between reconstruction quality and resource requirements. While recent deep learning methods achieve state-of-the-art performance, they typically rely on over…
An efficient spatial regularization method using superpixel segmentation and graph Laplacian regularization is proposed for sparse hyperspectral unmixing method. Since it is likely to find spectrally similar pixels in a homogeneous region,…