Related papers: Noise Variance Estimation Using Asymptotic Residua…

Suppose $L$ simultaneous independent stochastic systems generate observations, where the observations from each system depend on the underlying parameter of that system. The observations are unlabeled (anonymized), in the sense that an…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…

Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…

We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…

The mathematical theory of super-resolution developed recently by Cand\`{e}s and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set…

In this paper, the traditional model based variational method and learning based algorithms are naturally integrated to address mixed noise removal problem. To be different from single type noise (e.g. Gaussian) removal, it is a challenge…

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…

We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…

For identifying the non-Gaussian impulsive noise systems, normalized LMP (NLMP) has been proposed to combat impulsive-inducing instability. However, the standard algorithm is without considering the inherent sparse structure distribution of…

We proposed a real time Total-Variation denosing method with an automatic choice of hyper-parameter $\lambda$, and the good performance of this method provides a large application field. In this article, we adapt the developed method to the…

Multichannel frequency estimation with incomplete data and miscellaneous noises arises in array signal processing, modal analysis, wireless communications, and so on. In this paper, we consider maximum-likelihood(-like) optimization methods…

Real-world applications such as magnetic resonance imaging with multiple coils, multi-user communication, and diffuse optical tomography often assume a linear model where several sparse signals sharing common sparse supports are acquired by…

We propose an adaptive training scheme for unsupervised medical image registration. Existing methods rely on image reconstruction as the primary supervision signal. However, nuisance variables (e.g. noise and covisibility), violation of the…

We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a…