Related papers: Variational Data Assimilation via Sparse Regulariz…
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…
Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013) introduced a novel regularization method for compressive imaging in the context of compressed sensing with coherent redundant dictionaries. The approach relies on the…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the…
State estimates from weak constraint 4D-Var data assimilation can vary significantly depending on the data and model error covariances. As a result, the accuracy of these estimates heavily depends on the correct specification of both model…
As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques,…
Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
Variational Data Assimilation (DA) has been broadly used in engineering problems for field reconstruction and prediction by performing a weighted combination of multiple sources of noisy data. In recent years, the integration of deep…
Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a…
Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…
This paper develops a computational framework for optimizing the parameters of data assimilation systems in order to improve their performance. The approach formulates a continuous meta-optimization problem for parameters; the…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of…
Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…
Data assimilation addresses the problem of identifying plausible state trajectories of dynamical systems given noisy or incomplete observations. In geosciences, it presents challenges due to the high-dimensionality of geophysical dynamical…
Domain Adaptation (DA) aims to generalize the classifier learned from the source domain to the target domain. Existing DA methods usually assume that rich labels could be available in the source domain. However, there are usually a large…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…
Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality…