Related papers: Regularized adaptive long autoregressive spectral …
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
This paper solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion which avoids linearized approximations altogether. Based on creating virtual synthetic measurements, the algorithm uses a linear time-…
A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms are derived in a simple, systematic, and integrated manner without requiring any background knowledge to the…
This paper considers the problem of fitting the parameters of a Kalman smoother to data. We formulate the Kalman smoothing problem with missing measurements as a constrained least squares problem and provide an efficient method to solve it…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients,…
A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven…
This paper focuses on adaptive control of the discrete-time linear quadratic regulator (adaptive LQR). Recent literature has made significant contributions in proving non-asymptotic convergence rates, but existing approaches have a few…
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…
We study forecasting capabilities of the methods of Singular Spectrum Analysis (SSA) and Local Approximation (LA). A practical implementation of these methods to several time series is described. Details of the algorithms of these methods…
We propose a novel framework for fitting additive quantile regression models, which provides well calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
Sharpness-Aware Minimization (SAM) has proven highly effective in improving model generalization in machine learning tasks. However, SAM employs a fixed hyperparameter associated with the regularization to characterize the sharpness of the…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
Combined optimization problems that couple data-fidelity and regularization terms arise naturally in a wide range of inverse problems. In this paper, we study an adaptive randomized averaging block extended Bregman-Kaczmarz (aRABEBK) method…
We introduce a synergistic approach to double-talk robust acoustic echo cancellation combining adaptive Kalman filtering with a deep neural network-based postfilter. The proposed algorithm overcomes the well-known limitations of Kalman…