4,733 research outputs found
Towards Building Deep Networks with Bayesian Factor Graphs
We propose a Multi-Layer Network based on the Bayesian framework of the
Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional
lattice. The Latent Variable Model (LVM) is the basic building block of a
quadtree hierarchy built on top of a bottom layer of random variables that
represent pixels of an image, a feature map, or more generally a collection of
spatially distributed discrete variables. The multi-layer architecture
implements a hierarchical data representation that, via belief propagation, can
be used for learning and inference. Typical uses are pattern completion,
correction and classification. The FGrn paradigm provides great flexibility and
modularity and appears as a promising candidate for building deep networks: the
system can be easily extended by introducing new and different (in cardinality
and in type) variables. Prior knowledge, or supervised information, can be
introduced at different scales. The FGrn paradigm provides a handy way for
building all kinds of architectures by interconnecting only three types of
units: Single Input Single Output (SISO) blocks, Sources and Replicators. The
network is designed like a circuit diagram and the belief messages flow
bidirectionally in the whole system. The learning algorithms operate only
locally within each block. The framework is demonstrated in this paper in a
three-layer structure applied to images extracted from a standard data set.Comment: Submitted for journal publicatio
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
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
Unsupervised Sparse Dirichlet-Net for Hyperspectral Image Super-Resolution
In many computer vision applications, obtaining images of high resolution in
both the spatial and spectral domains are equally important. However, due to
hardware limitations, one can only expect to acquire images of high resolution
in either the spatial or spectral domains. This paper focuses on hyperspectral
image super-resolution (HSI-SR), where a hyperspectral image (HSI) with low
spatial resolution (LR) but high spectral resolution is fused with a
multispectral image (MSI) with high spatial resolution (HR) but low spectral
resolution to obtain HR HSI. Existing deep learning-based solutions are all
supervised that would need a large training set and the availability of HR HSI,
which is unrealistic. Here, we make the first attempt to solving the HSI-SR
problem using an unsupervised encoder-decoder architecture that carries the
following uniquenesses. First, it is composed of two encoder-decoder networks,
coupled through a shared decoder, in order to preserve the rich spectral
information from the HSI network. Second, the network encourages the
representations from both modalities to follow a sparse Dirichlet distribution
which naturally incorporates the two physical constraints of HSI and MSI.
Third, the angular difference between representations are minimized in order to
reduce the spectral distortion. We refer to the proposed architecture as
unsupervised Sparse Dirichlet-Net, or uSDN. Extensive experimental results
demonstrate the superior performance of uSDN as compared to the
state-of-the-art.Comment: Accepted by The IEEE Conference on Computer Vision and Pattern
Recognition (CVPR 2018, Spotlight
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