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Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…
A recent trend in Non-Rigid Structure-from-Motion (NRSfM) is to express local, differential constraints between pairs of images, from which the surface normal at any point can be obtained by solving a system of polynomial equations. The…
Reduced rank regression (RRR) is a fundamental tool for modeling multiple responses through low-dimensional latent structures, offering both interpretability and strong predictive performance in high-dimensional settings. Classical RRR…
Regression discontinuity (RD) is a widely used quasi-experimental design for causal inference. In the standard RD, the assignment to treatment is determined by a continuous pretreatment variable (i.e., running variable) falling above or…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Previous super-resolution reconstruction (SR) works are always designed on the assumption that the degradation operation is fixed, such as bicubic downsampling. However, as for remote sensing images, some unexpected factors can cause the…
In this paper, we propose a convex optimization-based estimation of sparse and smooth power spectral densities (PSDs) of complex-valued random processes from mixtures of realizations. While the PSDs are related to the magnitude of the…
The mathematical theory of super-resolution developed recently by Cand\`{e}s and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set…
We study average-reward Markov decision processes (AMDPs) and develop novel first-order methods with strong theoretical guarantees for both policy optimization and policy evaluation. Compared with intensive research efforts in finite sample…
This paper studies the mismatch removal problem, which may serve as the subsequent step of feature matching. Non-rigid deformation makes it difficult to remove mismatches because no parametric transformation can be found. To solve this…
The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boull\'e and…
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…
In this paper, we propose a Riemannian steepest descent method for solving a blind deconvolution problem. We prove that the proposed algorithm with an appropriate initialization will recover the exact solution with high probability when the…
We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a…
A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…
This paper presents an efficient optimization technique for gridless {2-D} line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which has been…
In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal…
Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the…
Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled…
The higher-order tensor renormalization group (HOTRG) is a fundamental method to calculate the physical quantities by using a tensor network representation. This method is based on the singular value decomposition (SVD) to take the…