The restricted total least squares problem: formulation, algorithm, and properties
SIAM Journal on Matrix Analysis and Applications
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Total Least Norm Formulation and Solution for Structured Problems
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Parameter Estimation in the Presence of Bounded Data Uncertainties
SIAM Journal on Matrix Analysis and Applications
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
Tikhonov Regularization and Total Least Squares
SIAM Journal on Matrix Analysis and Applications
Fast Transforms: Algorithms, Analyses, Applications
Fast Transforms: Algorithms, Analyses, Applications
Digital Image Restoration
Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem
SIAM Journal on Matrix Analysis and Applications
Efficient Algorithms for Solution of Regularized Total Least Squares
SIAM Journal on Matrix Analysis and Applications
Block-Toeplitz/Hankel Structured Total Least Squares
SIAM Journal on Matrix Analysis and Applications
A Global Solution for the Structured Total Least Squares Problem with Block Circulant Matrices
SIAM Journal on Matrix Analysis and Applications
On the Solution of the Tikhonov Regularization of the Total Least Squares Problem
SIAM Journal on Optimization
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints
SIAM Journal on Optimization
Overview of total least-squares methods
Signal Processing
The matrix-restricted total least-squares problem
Signal Processing
Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound
Foundations and Trends in Signal Processing
Robust mean-squared error estimation in the presence of model uncertainties
IEEE Transactions on Signal Processing
Linear Regression With Gaussian Model Uncertainty: Algorithms and Bounds
IEEE Transactions on Signal Processing
Minimax estimation of deterministic parameters in linear models with a random model matrix
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
Linear inverse problems with uncertain measurement matrices appear in many different applications. One of the standard techniques for solving such problems is the total least squares (TLS) method. Recently, an alternative approach has been suggested, based on maximizing an appropriate likelihood function assuming that the measurement matrix consists of random Gaussian variables. We refer to this technique as the total maximum likelihood (TML) method. Here we extend this strategy to the case in which the measurement matrix is structured so that the perturbations are not arbitrary but rather follow a fixed pattern. The resulting estimate is referred to as the structured TML (STML). As we show, the STML can be viewed as a regularized version of the structured TLS (STLS) approach in which the regularization consists of a logarithmic penalty. In contrast to the STLS solution, the STML always exists. Furthermore, its performance in practice tends to be superior to that of the STLS and competitive to other regularized solvers, as we illustrate via several examples. We also consider a few interesting special cases in which the STML can be computed efficiently either by reducing it into a one-dimensional problem regardless of the problem size or by a decomposition via a discrete Fourier transform.