9,277 research outputs found
Multi-modal dictionary learning for image separation with application in art investigation
In support of art investigation, we propose a new source separation method
that unmixes a single X-ray scan acquired from double-sided paintings. In this
problem, the X-ray signals to be separated have similar morphological
characteristics, which brings previous source separation methods to their
limits. Our solution is to use photographs taken from the front and back-side
of the panel to drive the separation process. The crux of our approach relies
on the coupling of the two imaging modalities (photographs and X-rays) using a
novel coupled dictionary learning framework able to capture both common and
disparate features across the modalities using parsimonious representations;
the common component models features shared by the multi-modal images, whereas
the innovation component captures modality-specific information. As such, our
model enables the formulation of appropriately regularized convex optimization
procedures that lead to the accurate separation of the X-rays. Our dictionary
learning framework can be tailored both to a single- and a multi-scale
framework, with the latter leading to a significant performance improvement.
Moreover, to improve further on the visual quality of the separated images, we
propose to train coupled dictionaries that ignore certain parts of the painting
corresponding to craquelure. Experimentation on synthetic and real data - taken
from digital acquisition of the Ghent Altarpiece (1432) - confirms the
superiority of our method against the state-of-the-art morphological component
analysis technique that uses either fixed or trained dictionaries to perform
image separation.Comment: submitted to IEEE Transactions on Images Processin
Sparsity and morphological diversity for hyperspectral data analysis
Recently morphological diversity and sparsity have
emerged as new and effective sources of diversity for
Blind Source Separation. Based on these new concepts,
novelmethods such as Generalized Morphological Component
Analysis have been put forward. The latter takes
advantage of the very sparse representation of structured
data in large overcomplete dictionaries, to separate
sources based on their morphology. Building on GMCA,
the purpose of this contribution is to describe a new algorithm
for hyperspectral data processing. Large-scale
hyperspectral data refers to collected data that exhibit
sparse spectral signatures in addition to sparse spatial
morphologies, in specified dictionaries of spectral and
spatial waveforms. Numerical experiments are reported
which demonstrate the validity of the proposed extension
for solving source separation problems involving
hyperspectral data
SZ and CMB reconstruction using Generalized Morphological Component Analysis
In the last decade, the study of cosmic microwave background (CMB) data has
become one of the most powerful tools to study and understand the Universe.
More precisely, measuring the CMB power spectrum leads to the estimation of
most cosmological parameters. Nevertheless, accessing such precious physical
information requires extracting several different astrophysical components from
the data. Recovering those astrophysical sources (CMB, Sunyaev-Zel'dovich
clusters, galactic dust) thus amounts to a component separation problem which
has already led to an intense activity in the field of CMB studies. In this
paper, we introduce a new sparsity-based component separation method coined
Generalized Morphological Component Analysis (GMCA). The GMCA approach is
formulated in a Bayesian maximum a posteriori (MAP) framework. Numerical
results show that this new source recovery technique performs well compared to
state-of-the-art component separation methods already applied to CMB data.Comment: 11 pages - Statistical Methodology - Special Issue on Astrostatistics
- in pres
WAVELET BASED NONLINEAR SEPARATION OF IMAGES
This work addresses a real-life problem corresponding
to the separation of the nonlinear mixture of images which
arises when we scan a paper document and the image from
the back page shows through.
The proposed solution consists of a non-iterative procedure
that is based on two simple observations: (1) the high
frequency content of images is sparse, and (2) the image
printed on each side of the paper appears more strongly in
the mixture acquired from that side than in the mixture acquired from the opposite side.
These ideas had already been used in the context of nonlinear denoising source separation (DSS). However, in that method the degree of separation achieved by applying these ideas was relatively weak, and the separation had to be improved by iterating within the DSS scheme. In this paper the application of these ideas is improved by changing the competition function and the wavelet transform that is used. These improvements allow us to achieve a good separation in one shot, without the need to integrate the process into an iterative DSS scheme. The resulting separation process is both nonlinear and non-local.
We present experimental results that show that the method
achieves a good separation quality
Underdetermined blind source separation based on Fuzzy C-Means and Semi-Nonnegative Matrix Factorization
Conventional blind source separation is based on over-determined with more sensors than sources but the underdetermined is a challenging case and more convenient to actual situation. Non-negative Matrix Factorization (NMF) has been widely applied to Blind Source Separation (BSS) problems. However, the separation results are sensitive to the initialization of parameters of NMF. Avoiding the subjectivity of choosing parameters, we used the Fuzzy C-Means (FCM) clustering technique to estimate the mixing matrix and to reduce the requirement for sparsity. Also, decreasing the constraints is regarded in this paper by using Semi-NMF. In this paper we propose a new two-step algorithm in order to solve the underdetermined blind source separation. We show how to combine the FCM clustering technique with the gradient-based NMF with the multi-layer technique. The simulation results show that our proposed algorithm can separate the source signals with high signal-to-noise ratio and quite low cost time compared with some algorithms
Sparse component separation for accurate CMB map estimation
The Cosmological Microwave Background (CMB) is of premier importance for the
cosmologists to study the birth of our universe. Unfortunately, most CMB
experiments such as COBE, WMAP or Planck do not provide a direct measure of the
cosmological signal; CMB is mixed up with galactic foregrounds and point
sources. For the sake of scientific exploitation, measuring the CMB requires
extracting several different astrophysical components (CMB, Sunyaev-Zel'dovich
clusters, galactic dust) form multi-wavelength observations. Mathematically
speaking, the problem of disentangling the CMB map from the galactic
foregrounds amounts to a component or source separation problem. In the field
of CMB studies, a very large range of source separation methods have been
applied which all differ from each other in the way they model the data and the
criteria they rely on to separate components. Two main difficulties are i) the
instrument's beam varies across frequencies and ii) the emission laws of most
astrophysical components vary across pixels. This paper aims at introducing a
very accurate modeling of CMB data, based on sparsity, accounting for beams
variability across frequencies as well as spatial variations of the components'
spectral characteristics. Based on this new sparse modeling of the data, a
sparsity-based component separation method coined Local-Generalized
Morphological Component Analysis (L-GMCA) is described. Extensive numerical
experiments have been carried out with simulated Planck data. These experiments
show the high efficiency of the proposed component separation methods to
estimate a clean CMB map with a very low foreground contamination, which makes
L-GMCA of prime interest for CMB studies.Comment: submitted to A&
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