Related papers: Telescoping Recursive Representations and Estimati…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…
We extend the criterion on the existence of telescopers for hypergeometric terms to the case of P-recursive sequences. This criterion is based on the concept of integral bases and the generalized Abramov-Petkovsek reduction for P-recursive…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…
The field of 3D reconstruction from images has rapidly evolved in the past few years, first with the introduction of Neural Radiance Field (NeRF) and more recently with 3D Gaussian Splatting (3DGS). The latter provides a significant edge…
We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the…
Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator,…
Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to…
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…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
We present a new technique - photon folding - for imaging in non-focusing telescopes. Motivated by the epoch-folding method in timing analysis, the photon folding technique directly provides the statistical significance of signals in…
Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
We present a probabilistic model for natural images which is based on Gaussian scale mixtures and a simple multiscale representation. In contrast to the dominant approach to modeling whole images focusing on Markov random fields, we…
We present a method to reconstruct dynamic scenes from monocular continuous-wave time-of-flight (C-ToF) cameras using raw sensor samples that achieves similar or better accuracy than neural volumetric approaches and is 100x faster. Quickly…
While 3D Gaussian splatting (3DGS) offers explicit and efficient scene representations for cone-beam computed tomography reconstruction, conventional photometric optimization inherently suffers from spectral bias under ultra sparse-view…
We consider Gaussian Random Fields on metric graphs defined implicitly as the stationary solution to a fractional SPDE driven by Gaussian white noise. Sampling from the finite element approximation requires the Cholesky factorization of 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…