385 research outputs found
A convex geometry based blind source separation method for separating nonnegative sources
This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hullspanned by the mapped observations. Considering these zerosamples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method
Convexity in source separation: Models, geometry, and algorithms
Source separation or demixing is the process of extracting multiple
components entangled within a signal. Contemporary signal processing presents a
host of difficult source separation problems, from interference cancellation to
background subtraction, blind deconvolution, and even dictionary learning.
Despite the recent progress in each of these applications, advances in
high-throughput sensor technology place demixing algorithms under pressure to
accommodate extremely high-dimensional signals, separate an ever larger number
of sources, and cope with more sophisticated signal and mixing models. These
difficulties are exacerbated by the need for real-time action in automated
decision-making systems.
Recent advances in convex optimization provide a simple framework for
efficiently solving numerous difficult demixing problems. This article provides
an overview of the emerging field, explains the theory that governs the
underlying procedures, and surveys algorithms that solve them efficiently. We
aim to equip practitioners with a toolkit for constructing their own demixing
algorithms that work, as well as concrete intuition for why they work
X-ray image separation via coupled dictionary learning
In support of art investigation, we propose a new source sepa- ration method
that unmixes a single X-ray scan acquired from double-sided paintings. Unlike
prior source separation meth- ods, which are based on statistical or structural
incoherence of the sources, we use visual images taken from the front- and
back-side of the panel to drive the separation process. The coupling of the two
imaging modalities is achieved via a new multi-scale dictionary learning
method. Experimental results demonstrate that our method succeeds in the
discrimination of the sources, while state-of-the-art methods fail to do so.Comment: To be presented at the IEEE International Conference on Image
Processing (ICIP), 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
Multichannel Source Separation Using Time-Deconvolutive CNMF
This paper addresses the separation of audio sources from convolutive mixtures captured by a microphone array. We approach the problem using complex-valued non-negative matrix factorization (CNMF), and extend previous works by tailoring advanced (single-channel) NMF models, such as the deconvolutive NMF, to the multichannel factorization setup. Further, a sparsity-promoting scheme is proposed so that the underlying estimated parameters better fit the time-frequency properties inherent in some audio sources. The proposed parameter estimation framework is compatible with previous related works, and can be thought of as a step toward a more general method. We evaluate the resulting separation accuracy using a simulated acoustic scenario, and the tests confirm that the proposed algorithm provides superior separation quality when compared to a state-of-the-art benchmark. Finally, an analysis of the effects of the introduced regularization term shows that the solution is in fact steered toward a sparser representation
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