2,141 research outputs found
Compressive Source Separation: Theory and Methods for Hyperspectral Imaging
With the development of numbers of high resolution data acquisition systems
and the global requirement to lower the energy consumption, the development of
efficient sensing techniques becomes critical. Recently, Compressed Sampling
(CS) techniques, which exploit the sparsity of signals, have allowed to
reconstruct signal and images with less measurements than the traditional
Nyquist sensing approach. However, multichannel signals like Hyperspectral
images (HSI) have additional structures, like inter-channel correlations, that
are not taken into account in the classical CS scheme. In this paper we exploit
the linear mixture of sources model, that is the assumption that the
multichannel signal is composed of a linear combination of sources, each of
them having its own spectral signature, and propose new sampling schemes
exploiting this model to considerably decrease the number of measurements
needed for the acquisition and source separation. Moreover, we give theoretical
lower bounds on the number of measurements required to perform reconstruction
of both the multichannel signal and its sources. We also proposed optimization
algorithms and extensive experimentation on our target application which is
HSI, and show that our approach recovers HSI with far less measurements and
computational effort than traditional CS approaches.Comment: 32 page
Sparse Signal Separation in Redundant Dictionaries
We formulate a unified framework for the separation of signals that are
sparse in "morphologically" different redundant dictionaries. This formulation
incorporates the so-called "analysis" and "synthesis" approaches as special
cases and contains novel hybrid setups. We find corresponding coherence-based
recovery guarantees for an l1-norm based separation algorithm. Our results
recover those reported in Studer and Baraniuk, ACHA, submitted, for the
synthesis setting, provide new recovery guarantees for the analysis setting,
and form a basis for comparing performance in the analysis and synthesis
settings. As an aside our findings complement the D-RIP recovery results
reported in Cand\`es et al., ACHA, 2011, for the "analysis" signal recovery
problem: minimize_x ||{\Psi}x||_1 subject to ||y - Ax||_2 \leq {\epsilon}, by
delivering corresponding coherence-based recovery results.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT),
Boston, MA, July 201
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
Compressed Sensing with Coherent and Redundant Dictionaries
This article presents novel results concerning the recovery of signals from
undersampled data in the common situation where such signals are not sparse in
an orthonormal basis or incoherent dictionary, but in a truly redundant
dictionary. This work thus bridges a gap in the literature and shows not only
that compressed sensing is viable in this context, but also that accurate
recovery is possible via an L1-analysis optimization problem. We introduce a
condition on the measurement/sensing matrix, which is a natural generalization
of the now well-known restricted isometry property, and which guarantees
accurate recovery of signals that are nearly sparse in (possibly) highly
overcomplete and coherent dictionaries. This condition imposes no incoherence
restriction on the dictionary and our results may be the first of this kind. We
discuss practical examples and the implications of our results on those
applications, and complement our study by demonstrating the potential of
L1-analysis for such problems
Generalized Inpainting Method for Hyperspectral Image Acquisition
A recently designed hyperspectral imaging device enables multiplexed
acquisition of an entire data volume in a single snapshot thanks to
monolithically-integrated spectral filters. Such an agile imaging technique
comes at the cost of a reduced spatial resolution and the need for a
demosaicing procedure on its interleaved data. In this work, we address both
issues and propose an approach inspired by recent developments in compressed
sensing and analysis sparse models. We formulate our superresolution and
demosaicing task as a 3-D generalized inpainting problem. Interestingly, the
target spatial resolution can be adjusted for mitigating the compression level
of our sensing. The reconstruction procedure uses a fast greedy method called
Pseudo-inverse IHT. We also show on simulations that a random arrangement of
the spectral filters on the sensor is preferable to regular mosaic layout as it
improves the quality of the reconstruction. The efficiency of our technique is
demonstrated through numerical experiments on both synthetic and real data as
acquired by the snapshot imager.Comment: Keywords: Hyperspectral, inpainting, iterative hard thresholding,
sparse models, CMOS, Fabry-P\'ero
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