1,619 research outputs found
Broadband angle of arrival estimation methods in a polynomial matrix decomposition framework
A large family of broadband angle of arrival estimation algorithms are based on the coherent signal subspace (CSS) method, whereby focussing matrices appropriately align covariance matrices across narrowband frequency bins. In this paper, we analyse an auto-focussing approach in the framework of polynomial covariance matrix decompositions, leading to comparisons to two recently proposed polynomial multiple signal classification (MUSIC) algorithms. The analysis is complemented with numerical simulations
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
On the non-existence of unbiased estimators in constrained estimation problems
We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then there exists no unbiased estimator.Weaker conditions for the absence of unbiased constrained estimators are also specified. We provide several examples which demonstrate the utility of these conditions
Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
Euclidean distance matrices (EDM) are matrices of squared distances between
points. The definition is deceivingly simple: thanks to their many useful
properties they have found applications in psychometrics, crystallography,
machine learning, wireless sensor networks, acoustics, and more. Despite the
usefulness of EDMs, they seem to be insufficiently known in the signal
processing community. Our goal is to rectify this mishap in a concise tutorial.
We review the fundamental properties of EDMs, such as rank or
(non)definiteness. We show how various EDM properties can be used to design
algorithms for completing and denoising distance data. Along the way, we
demonstrate applications to microphone position calibration, ultrasound
tomography, room reconstruction from echoes and phase retrieval. By spelling
out the essential algorithms, we hope to fast-track the readers in applying
EDMs to their own problems. Matlab code for all the described algorithms, and
to generate the figures in the paper, is available online. Finally, we suggest
directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine
- change of title in the last revisio
On the non-existence of unbiased estimators in constrained estimation problems
We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then there exists no unbiased estimator.Weaker conditions for the absence of unbiased constrained estimators are also specified. We provide several examples which demonstrate the utility of these conditions
Non-uniform Array and Frequency Spacing for Regularization-free Gridless DOA
Gridless direction-of-arrival (DOA) estimation with multiple frequencies can
be applied in acoustics source localization problems. We formulate this as an
atomic norm minimization (ANM) problem and derive an equivalent
regularization-free semi-definite program (SDP) thereby avoiding regularization
bias. The DOA is retrieved using a Vandermonde decomposition on the Toeplitz
matrix obtained from the solution of the SDP.
We also propose a fast SDP program to deal with non-uniform array and
frequency spacing. For non-uniform spacings, the Toeplitz structure will not
exist, but the DOA is retrieved via irregular Vandermonde decomposition (IVD),
and we theoretically guarantee the existence of the IVD. We extend ANM to the
multiple measurement vector (MMV) cases and derive its equivalent
regularization-free SDP. Using multiple frequencies and the MMV model, we can
resolve more sources than the number of physical sensors for a uniform linear
array. Numerical results demonstrate that the regularization-free framework is
robust to noise and aliasing, and it overcomes the regularization bias
Location-free Spectrum Cartography
Spectrum cartography constructs maps of metrics such as channel gain or
received signal power across a geographic area of interest using spatially
distributed sensor measurements. Applications of these maps include network
planning, interference coordination, power control, localization, and cognitive
radios to name a few. Since existing spectrum cartography techniques require
accurate estimates of the sensor locations, their performance is drastically
impaired by multipath affecting the positioning pilot signals, as occurs in
indoor or dense urban scenarios. To overcome such a limitation, this paper
introduces a novel paradigm for spectrum cartography, where estimation of
spectral maps relies on features of these positioning signals rather than on
location estimates. Specific learning algorithms are built upon this approach
and offer a markedly improved estimation performance than existing approaches
relying on localization, as demonstrated by simulation studies in indoor
scenarios.Comment: 14 pages, 12 figures, 1 table. Submitted to IEEE Transactions on
Signal Processin
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