Related papers: Nonparametric Denoising of Signals with Unknown Lo…
We consider the problem of recovering a latent signal $X$ from its noisy observation $Y$. The unknown law $\mathbb{P}^X$ of $X$, and in particular its support $\mathscr{M}$, are accessible only through a large sample of i.i.d.\…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
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…
Signal detection in environments with unknown signal bandwidth and time intervals is a fundamental problem in adversarial and spectrum-sharing scenarios. This paper addresses the problem of detecting signals occupying unknown degrees of…
In all applications in digital communications, it is crucial for an estimator to be unbiased. Although so-called soft feedback is widely employed in many different fields of engineering, typically the biased estimate is used. In this paper,…
While deep learning offers powerful capabilities for scientific research, its application is often hindered by a lack of quantitative reliability. To address this, we introduce a probabilistic denoising framework that simultaneously…
Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially…
In this paper we study the problem of recovering a structured but unknown parameter ${\bf{\theta}}^*$ from $n$ nonlinear observations of the form $y_i=f(\langle {\bf{x}}_i,{\bf{\theta}}^*\rangle)$ for $i=1,2,\ldots,n$. We develop a…
In this paper, we consider the problem of recovering an unknown sparse signal $\xv_0 \in \mathbb{R}^n$ from noisy linear measurements $\yv = \Hm \xv_0+ \zv \in \mathbb{R}^m$. A popular approach is to solve the $\ell_1$-norm regularized…
Recovering complex-valued image recovery from noisy indirect data is important in applications such as ultrasound imaging and synthetic aperture radar. While there are many effective algorithms to recover point estimates of the magnitude,…
In this technical communique, we propose a novel observer-based adaptive scheme to deal with the parameter estimation problem of biased sinusoidal signals. Different from the existing adaptive frequency estimation scheme, the proposed…
Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies…
In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample…
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…
We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon$. We assume that $f$ belongs to a class of smooth functions ${\cal F}^d\subset…
Frequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured…
In this paper, we present an optimal filter for linear time-varying continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. We first show that the unknown inputs…
A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic…