Related papers: Efficient Preconditioning for Noisy Separable NMFs…
The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled…
Recently, a family of tractable NMF algorithms have been proposed under the assumption that the data matrix satisfies a separability condition Donoho & Stodden (2003); Arora et al. (2012). Geometrically, this condition reformulates the NMF…
We present a new deep learning paradigm for the generation of sparse approximate inverse (SPAI) preconditioners for matrix systems arising from the mesh-based discretization of elliptic differential operators. Our approach is based upon the…
The performance of speaker-related systems usually degrades heavily in practical applications largely due to the presence of background noise. To improve the robustness of such systems in unknown noisy environments, this paper proposes a…
Given an affine space of matrices $\mathcal{L}$ and a matrix $\Theta\in \mathcal{L}$, consider the problem of computing the closest rank deficient matrix to $\Theta$ on $\mathcal{L}$ with respect to the Frobenius norm. This is a nonconvex…
The core challenge of hyperspectral image denoising is striking the right balance between data fidelity and noise prior modeling. Most existing methods place too much emphasis on the intrinsic priors of the image while overlooking diverse…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…
Magnetic resonance imaging (MRI) is a non-invasive medical imaging technique offering high-resolution 3D images and valuable insights into human tissue conditions. Even at present, the refinement of denoising methods for MRI remains a…
In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex…
In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based…
Noise synthesis is a promising solution for addressing the data shortage problem in data-driven low-light RAW image denoising. However, accurate noise synthesis methods often necessitate labor-intensive calibration and profiling procedures…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function…
This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…
Balanced Singular Perturbation Approximation (SPA) is a model order reduction method for linear time-invariant systems that guarantees asymptotic stability and for which there exists an a priori error bound. In that respect, it is similar…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…