25,741 research outputs found
Blind Minimax Estimation
We consider the linear regression problem of estimating an unknown,
deterministic parameter vector based on measurements corrupted by colored
Gaussian noise. We present and analyze blind minimax estimators (BMEs), which
consist of a bounded parameter set minimax estimator, whose parameter set is
itself estimated from measurements. Thus, one does not require any prior
assumption or knowledge, and the proposed estimator can be applied to any
linear regression problem. We demonstrate analytically that the BMEs strictly
dominate the least-squares estimator, i.e., they achieve lower mean-squared
error for any value of the parameter vector. Both Stein's estimator and its
positive-part correction can be derived within the blind minimax framework.
Furthermore, our approach can be readily extended to a wider class of
estimation problems than Stein's estimator, which is defined only for white
noise and non-transformed measurements. We show through simulations that the
BMEs generally outperform previous extensions of Stein's technique.Comment: 12 pages, 7 figure
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
Extracting individual contributions from their mixture: a blind source separation approach, with examples from space and laboratory plasmas
Multipoint or multichannel observations in plasmas can frequently be modelled
as an instantaneous mixture of contributions (waves, emissions, ...) of
different origins. Recovering the individual sources from their mixture then
becomes one of the key objectives. However, unless the underlying mixing
processes are well known, these situations lead to heavily underdetermined
problems. Blind source separation aims at disentangling such mixtures with the
least possible prior information on the sources and their mixing processes.
Several powerful approaches have recently been developed, which can often
provide new or deeper insight into the underlying physics. This tutorial paper
briefly discusses some possible applications of blind source separation to the
field of plasma physics, in which this concept is still barely known. Two
examples are given. The first one shows how concurrent processes in the
dynamical response of the electron temperature in a tokamak can be separated.
The second example deals with solar spectral imaging in the Extreme UV and
shows how empirical temperature maps can be built.Comment: expanded version of an article to appear in Contributions to Plasma
Physics (2010
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