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High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…
Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations,…
In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…
The subspace approximation problem with outliers, for given $n$ points in $d$ dimensions $x_{1},\ldots, x_{n} \in R^{d}$, an integer $1 \leq k \leq d$, and an outlier parameter $0 \leq \alpha \leq 1$, is to find a $k$-dimensional linear…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
A popular paradigm for 3D point cloud registration is by extracting 3D keypoint correspondences, then estimating the registration function from the correspondences using a robust algorithm. However, many existing 3D keypoint techniques tend…
We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation…
This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…
Anomalies (or outliers) are prevalent in real-world empirical observations and potentially mask important underlying structures. Accurate identification of anomalous samples is crucial for the success of downstream data analysis tasks. To…
Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed…
Robust regression models in the presence of outliers have significant practical relevance in areas such as signal processing, financial econometrics, and energy management. Many existing robust regression methods, either grounded in…
Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least-squares…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
Rotation search and point cloud registration are two fundamental problems in robotics and computer vision, which aim to estimate the rotation and the transformation between the 3D vector sets and point clouds, respectively. Due to the…
Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable…
Traditional image registration methods are robust but slow due to their iterative nature. While deep learning has accelerated inference, it often struggles with domain shifts. Emerging registration foundation models offer a balance of speed…
The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…
In robotic inspection, joint registration of multiple point clouds is an essential technique for estimating the transformation relationships between measured parts, such as multiple blades in a propeller. However, the presence of noise and…
This paper proposes a theoretical framework to address the reduced biquaternion equality-constrained total least squares (RBTLSE) problem. The objective is to find an approximate solution to the system $AX \approx B$, subject to linear…