Related papers: A Statistical Framework and Analysis for Perfect R…
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
A popular class of lidar-based grid mapping algorithms computes for each map cell the probability that it reflects an incident laser beam. These algorithms typically determine the map as the set of reflection probabilities that maximizes…
This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…
This paper proposes a novel approach to robust radar detection of range-spread targets embedded in Gaussian noise with unknown covariance matrix. The idea is to model the useful target echo in each range cell as the sum of a coherent signal…
It is widely believed that range resolution, the ability to distinguish between two closely situated targets, depends inversely on the bandwidth of the transmitted radar signal. Here we demonstrate a different type of ranging system, which…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterisation, that have been…
We study the target parameter estimation for sub-Nyquist pulse-Doppler radar. Several past works have addressed this problem but either have low estimation accuracy for off-grid targets, take large computation load, or lack versatility for…
With the increasing popularity of human-computer interaction applications, there is also growing interest in generating sufficiently large and diverse data sets for automatic radar-based recognition of hand poses and gestures. Radar…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…
Many experiments utilize the precession of trapped particles in magnetic fields to perform high precision measurements. It had been presumed that after free precession, initially polarized particles will form a Gaussian phase distribution…
Radar sounders are electromagnetic instruments that can probe deep into the subsurface of Earth and other planetary bodies by processing the echo of transmitted radar waves. Conventional approaches for analyzing such data rely on…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining…