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A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral…
Finite Rate of Innovation (FRI) sampling theory enables reconstruction of classes of continuous non-bandlimited signals that have a small number of free parameters from their low-rate discrete samples. This task is often translated into a…
The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity…
We propose a model-agnostic pipeline to recover graph signals from an expert system by exploiting the content addressable memory property of restricted Boltzmann machine and the representational ability of a neural network. The proposed…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
In this paper, we propose a new test for the detection of a change in a non-linear (auto-)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at-most-one-change…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…
High resolution images can be acquired using a non-regular sampling sensor which consists of an underlying low resolution sensor that is covered with a non-regular sampling mask. The reconstructed high resolution image is then obtained…
We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…
The autoregressive time series model is a popular second-order stationary process, modeling a wide range of real phenomena. However, in applications, autoregressive signals are often corrupted by additive noise. Further, the autoregressive…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
Common ISAR radar images and signals can be reconstructed from much fewer samples than the sampling theorem requires since they are usually sparse. Unavailable randomly positioned samples can result from heavily corrupted parts of the…
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a…
We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…