Related papers: Error Processing of Sparse Identification of Nonli…
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
Identifying governing equations in physical and biological systems from datasets remains a long-standing challenge across various scientific disciplines, providing mechanistic insights into complex system evolution. Common methods like…
We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…
We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field contain some a priori assumptions about the error corrupting…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
Sparse system identification problems often exist in many applications, such as echo interference cancellation, sparse channel estimation, and adaptive beamforming. One of popular adaptive sparse system identification (ASSI) methods is…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…
This paper presents a new method, referred to here as the sparsity invariant transformation based $\ell_1$ minimization, to solve the $\ell_0$ minimization problem for an over-determined linear system corrupted by additive sparse errors…
Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality…
Measured data from a dynamical system can be assimilated into a predictive model by means of Kalman filters. Nonlinear extensions of the Kalman filter, such as the Extended Kalman Filter (EKF), are required to enable the joint estimation of…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…
This paper develops a sparsity-promoting integral concurrent learning (SP-ICL) adaptation law for a linearly parametrized uncertain nonlinear control-affine system. The unknown parameters are learned using ICL with sparsity-promoting…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…