632 research outputs found
Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing
In hyperspectral images, some spectral bands suffer from low signal-to-noise
ratio due to noisy acquisition and atmospheric effects, thus requiring robust
techniques for the unmixing problem. This paper presents a robust supervised
spectral unmixing approach for hyperspectral images. The robustness is achieved
by writing the unmixing problem as the maximization of the correntropy
criterion subject to the most commonly used constraints. Two unmixing problems
are derived: the first problem considers the fully-constrained unmixing, with
both the non-negativity and sum-to-one constraints, while the second one deals
with the non-negativity and the sparsity-promoting of the abundances. The
corresponding optimization problems are solved efficiently using an alternating
direction method of multipliers (ADMM) approach. Experiments on synthetic and
real hyperspectral images validate the performance of the proposed algorithms
for different scenarios, demonstrating that the correntropy-based unmixing is
robust to outlier bands.Comment: 23 page
Non-convex regularization in remote sensing
In this paper, we study the effect of different regularizers and their
implications in high dimensional image classification and sparse linear
unmixing. Although kernelization or sparse methods are globally accepted
solutions for processing data in high dimensions, we present here a study on
the impact of the form of regularization used and its parametrization. We
consider regularization via traditional squared (2) and sparsity-promoting (1)
norms, as well as more unconventional nonconvex regularizers (p and Log Sum
Penalty). We compare their properties and advantages on several classification
and linear unmixing tasks and provide advices on the choice of the best
regularizer for the problem at hand. Finally, we also provide a fully
functional toolbox for the community.Comment: 11 pages, 11 figure
Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization
Principal component analysis (PCA) is widely used for dimensionality
reduction, with well-documented merits in various applications involving
high-dimensional data, including computer vision, preference measurement, and
bioinformatics. In this context, the fresh look advocated here permeates
benefits from variable selection and compressive sampling, to robustify PCA
against outliers. A least-trimmed squares estimator of a low-rank bilinear
factor analysis model is shown closely related to that obtained from an
-(pseudo)norm-regularized criterion encouraging sparsity in a matrix
explicitly modeling the outliers. This connection suggests robust PCA schemes
based on convex relaxation, which lead naturally to a family of robust
estimators encompassing Huber's optimal M-class as a special case. Outliers are
identified by tuning a regularization parameter, which amounts to controlling
sparsity of the outlier matrix along the whole robustification path of (group)
least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its
neat ties to robust statistics, the developed outlier-aware PCA framework is
versatile to accommodate novel and scalable algorithms to: i) track the
low-rank signal subspace robustly, as new data are acquired in real time; and
ii) determine principal components robustly in (possibly) infinite-dimensional
feature spaces. Synthetic and real data tests corroborate the effectiveness of
the proposed robust PCA schemes, when used to identify aberrant responses in
personality assessment surveys, as well as unveil communities in social
networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin
Sparse and Non-Negative BSS for Noisy Data
Non-negative blind source separation (BSS) has raised interest in various
fields of research, as testified by the wide literature on the topic of
non-negative matrix factorization (NMF). In this context, it is fundamental
that the sources to be estimated present some diversity in order to be
efficiently retrieved. Sparsity is known to enhance such contrast between the
sources while producing very robust approaches, especially to noise. In this
paper we introduce a new algorithm in order to tackle the blind separation of
non-negative sparse sources from noisy measurements. We first show that
sparsity and non-negativity constraints have to be carefully applied on the
sought-after solution. In fact, improperly constrained solutions are unlikely
to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA
(non-negative Generalized Morphological Component Analysis), makes use of
proximal calculus techniques to provide properly constrained solutions. The
performance of nGMCA compared to other state-of-the-art algorithms is
demonstrated by numerical experiments encompassing a wide variety of settings,
with negligible parameter tuning. In particular, nGMCA is shown to provide
robustness to noise and performs well on synthetic mixtures of real NMR
spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal
Processin
Brain covariance selection: better individual functional connectivity models using population prior
Spontaneous brain activity, as observed in functional neuroimaging, has been
shown to display reproducible structure that expresses brain architecture and
carries markers of brain pathologies. An important view of modern neuroscience
is that such large-scale structure of coherent activity reflects modularity
properties of brain connectivity graphs. However, to date, there has been no
demonstration that the limited and noisy data available in spontaneous activity
observations could be used to learn full-brain probabilistic models that
generalize to new data. Learning such models entails two main challenges: i)
modeling full brain connectivity is a difficult estimation problem that faces
the curse of dimensionality and ii) variability between subjects, coupled with
the variability of functional signals between experimental runs, makes the use
of multiple datasets challenging. We describe subject-level brain functional
connectivity structure as a multivariate Gaussian process and introduce a new
strategy to estimate it from group data, by imposing a common structure on the
graphical model in the population. We show that individual models learned from
functional Magnetic Resonance Imaging (fMRI) data using this population prior
generalize better to unseen data than models based on alternative
regularization schemes. To our knowledge, this is the first report of a
cross-validated model of spontaneous brain activity. Finally, we use the
estimated graphical model to explore the large-scale characteristics of
functional architecture and show for the first time that known cognitive
networks appear as the integrated communities of functional connectivity graph.Comment: in Advances in Neural Information Processing Systems, Vancouver :
Canada (2010
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
Nearfield Acoustic Holography using sparsity and compressive sampling principles
Regularization of the inverse problem is a complex issue when using
Near-field Acoustic Holography (NAH) techniques to identify the vibrating
sources. This paper shows that, for convex homogeneous plates with arbitrary
boundary conditions, new regularization schemes can be developed, based on the
sparsity of the normal velocity of the plate in a well-designed basis, i.e. the
possibility to approximate it as a weighted sum of few elementary basis
functions. In particular, these new techniques can handle discontinuities of
the velocity field at the boundaries, which can be problematic with standard
techniques. This comes at the cost of a higher computational complexity to
solve the associated optimization problem, though it remains easily tractable
with out-of-the-box software. Furthermore, this sparsity framework allows us to
take advantage of the concept of Compressive Sampling: under some conditions on
the sampling process (here, the design of a random array, which can be
numerically and experimentally validated), it is possible to reconstruct the
sparse signals with significantly less measurements (i.e., microphones) than
classically required. After introducing the different concepts, this paper
presents numerical and experimental results of NAH with two plate geometries,
and compares the advantages and limitations of these sparsity-based techniques
over standard Tikhonov regularization.Comment: Journal of the Acoustical Society of America (2012
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