相关论文: Priorconditioned Sparsity-Promoting Projection Met…

Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem.…

When solving ill-posed inverse problems, a good choice of the prior is critical for the computation of a reasonable solution. A common approach is to include a Gaussian prior, which is defined by a mean vector and a symmetric and positive…

Linear precoding techniques can achieve near- optimal capacity due to the special channel property in down- link massive MIMO systems, but involve high complexity since complicated matrix inversion of large size is required. In this paper,…

Many large-scale stochastic optimization algorithms involve repeated solutions of linear systems or evaluations of log-determinants. In these regimes, computing exact solutions is often unnecessary; it is more computationally efficient to…

In the present work, we propose new tensor Krylov subspace method for ill posed linear tensor problems such as in color or video image restoration. Those methods are based on the tensor-tensor discrete cosine transform that gives fast…

Reconstructing objects from posed images is a crucial and complex task in computer graphics and computer vision. While NeRF-based neural reconstruction methods have exhibited impressive reconstruction ability, they tend to be…

Accurate reconstruction and relighting of glossy objects remains a longstanding challenge, as object shape, material properties, and illumination are inherently difficult to disentangle. Existing neural rendering approaches often rely on…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

We are concerned with a novel Bayesian statistical framework for the characterization of natural subsurface formations, a very challenging task. Because of the large dimension of the stochastic space of the prior distribution in the…

Implicit neural representations (INRs) have achieved remarkable success in image representation and compression, but they require substantial training time and memory. Meanwhile, recent 2D Gaussian Splatting (GS) methods (\textit{e.g.},…

This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key components of the proposed method consist of the localization…

3D Gaussian Splatting (3DGS) is a leading 3D scene reconstruction method, obtaining high-quality reconstruction with real-time rendering runtime performance. The main idea behind 3DGS is to represent the scene as a collection of 3D…

In this paper we present general-purpose preconditioners for regularized augmented systems arising from optimization problems, and their corresponding normal equations. We discuss positive definite preconditioners, suitable for CG and…

For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…

A modification of the generalized shift-splitting (GSS) method is presented for solving singular saddle point problems. In this kind of modification, the diagonal shift matrix is replaced by a block diagonal matrix which is symmetric…

Sparse-view satellite image surface reconstruction remains highly challenging, fundamentally because the reliability of multi-view matching under satellite imaging conditions is strongly spatially heterogeneous. Affected by large…

In this paper the problem of restoration of non-negative sparse signals is addressed in the Bayesian framework. We introduce a new probabilistic hierarchical prior, based on the Generalized Hyperbolic (GH) distribution, which explicitly…

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…

Gaussian Splatting demonstrates impressive results in multi-view reconstruction based on Gaussian explicit representations. However, the current Gaussian primitives only have a single view-dependent color and an opacity to represent the…