963 research outputs found
On Time-Reversal Imaging by Statistical Testing
This letter is focused on the design and analysis of computational wideband
time-reversal imaging algorithms, designed to be adaptive with respect to the
noise levels pertaining to the frequencies being employed for scene probing.
These algorithms are based on the concept of cell-by-cell processing and are
obtained as theoretically-founded decision statistics for testing the
hypothesis of single-scatterer presence (absence) at a specific location. These
statistics are also validated in comparison with the maximal invariant
statistic for the proposed problem.Comment: Reduced form accepted in IEEE Signal Processing Letter
A Unifying Framework for Adaptive Radar Detection in Homogeneous plus Structured Interference-Part II: Detectors Design
This paper deals with the problem of adaptive multidimensional/multichannel
signal detection in homogeneous Gaussian disturbance with unknown covariance
matrix and structured (unknown) deterministic interference. The aforementioned
problem extends the well-known Generalized Multivariate Analysis of Variance
(GMANOVA) tackled in the open literature. In a companion paper, we have
obtained the Maximal Invariant Statistic (MIS) for the problem under
consideration, as an enabling tool for the design of suitable detectors which
possess the Constant False-Alarm Rate (CFAR) property. Herein, we focus on the
development of several theoretically-founded detectors for the problem under
consideration. First, all the considered detectors are shown to be function of
the MIS, thus proving their CFARness property. Secondly, coincidence or
statistical equivalence among some of them in such a general signal model is
proved. Thirdly, strong connections to well-known simpler scenarios found in
adaptive detection literature are established. Finally, simulation results are
provided for a comparison of the proposed receivers.Comment: Submitted for journal publicatio
A Theory of Cramer-Rao Bounds for Constrained Parametric Models
A simple expression for the Cram'er-Rao bound (CRB) is presented for the scenario of estimating parameters that are required to satisfy a differentiable constraint function . A proof of this constrained CRB (CCRB) is provided using the implicit function theorem, and the encompassing theory of the CCRB is proven in a similar manner. This theory includes connecting the CCRB to notions of identifiability of constrained parameters; the linear model under a linear constraint; the constrained maximum likelihood problem, it's asymptotic properties and the method of scoring with constraints; and hypothesis testing. The value of the tools developed in this theory are then presented in the communications context for the convolutive mixture model and the calibrated array model
Cram\'er-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI
We extend the traditional framework for estimating subspace bases that
maximize the preserved signal energy to additionally preserve the Cram\'er-Rao
bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and
precision in the quantitative maps. To this end, we introduce an
\textit{approximate compressed CRB} based on orthogonalized versions of the
signal's derivatives with respect to the model parameters. This approximation
permits singular value decomposition (SVD)-based minimization of both the CRB
and signal losses during compression. Compared to the traditional SVD approach,
the proposed method better preserves the CRB across all biophysical parameters
with negligible cost to the preserved signal energy, leading to reduced bias
and variance of the parameter estimates in simulation. In vivo, improved
accuracy and precision are observed in two quantitative neuroimaging
applications, permitting the use of smaller basis sizes in subspace
reconstruction and offering significant computational savings
Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
There are three equivalent ways of representing two jointly observed
real-valued signals: as a bivariate vector signal, as a single complex-valued
signal, or as two analytic signals known as the rotary components. Each
representation has unique advantages depending on the system of interest and
the application goals. In this paper we provide a joint framework for all three
representations in the context of frequency-domain stochastic modeling. This
framework allows us to extend many established statistical procedures for
bivariate vector time series to complex-valued and rotary representations.
These include procedures for parametrically modeling signal coherence,
estimating model parameters using the Whittle likelihood, performing
semi-parametric modeling, and choosing between classes of nested models using
model choice. We also provide a new method of testing for impropriety in
complex-valued signals, which tests for noncircular or anisotropic second-order
statistical structure when the signal is represented in the complex plane.
Finally, we demonstrate the usefulness of our methodology in capturing the
anisotropic structure of signals observed from fluid dynamic simulations of
turbulence.Comment: To appear in IEEE Transactions on Signal Processin
Interfering Channel Estimation for Radar and Communication Coexistence
We investigate the interfering channel estimation in radar and communication coexistence, where a multi-input-multi-output (MIMO) radar is operated in a “search and track” mode, and a MIMO base station (BS) is attempting to acquire the interfering channel state information (ICSI) between them, which is required for the precoding designs. In contrast to conventional training based techniques, we exploit radar probing waveforms as pilot signals, which requires no coordination between the systems. As the radar randomly transmits searching and tracking waveforms, it is challenging for the BS to directly obtain the ICSI. We therefore propose a Rao test approach to firstly identify the working mode of the radar, and then estimate the channel. We further provide theoretical performance analysis for the Rao detector. Finally, we assess the effectiveness of the proposed approach by numerical simulations, which show that the BS is able to estimate the ICSI with limited information from the radar
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
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