Related papers: An automatic L1-based regularization method for th…

In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…

We consider the identification of spatially distributed parameters under $H^1$ regularization. Solving the associated minimization problem by Gauss-Newton iteration results in linearized problems to be solved in each step that can be cast…

Automated material model discovery disrupts the tedious and time-consuming cycle of iteratively calibrating and modifying manually designed models. Non-smooth L1-norm regularization is the backbone of automated model discovery; however, the…

In this work we introduce a comprehensive algorithmic pipeline for multiple parametric model estimation. The proposed approach analyzes the information produced by a random sampling algorithm (e.g., RANSAC) from a machine…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…

When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…

We present a converged algorithm for Tikhonov regularized nonnegative matrix factorization (NMF). We specially choose this regularization because it is known that Tikhonov regularized least square (LS) is the more preferable form in solving…

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference…

This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with…

Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…

We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…

This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…

In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An…

A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be…

We develop a Levenberg-Marquardt method for minimizing the sum of a smooth nonlinear least-squar es term $f(x) = \tfrac{1}{2} \|F(x)\|_2^2$ and a nonsmooth term $h$. Both $f$ and $h$ may be nonconvex. Steps are computed by minimizing the…

A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be…

Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…

$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…

A pilot project has been proceeded to map 1 deg$^2$ on the Galactic plane for radio recombination lines (RRLs) using the Five hundred meter Aperture Spherical Telescope (FAST). The motivation is to verify the techniques and reliabilities…