4,253 research outputs found
On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations
Considered herein are the generalized Camassa-Holm and Degasperis-Procesi
equations in the spatially periodic setting. The precise blow-up scenarios of
strong solutions are derived for both of equations. Several conditions on the
initial data guaranteeing the development of singularities in finite time for
strong solutions of these two equations are established. The exact blow-up
rates are also determined. Finally, geometric descriptions of these two
integrable equations from non-stretching invariant curve flows in
centro-equiaffine geometries, pseudo-spherical surfaces and affine surfaces are
given.Comment: 26 page
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
Hyperspectral Image Analysis through Unsupervised Deep Learning
Hyperspectral image (HSI) analysis has become an active research area in computer vision field with a wide range of applications. However, in order to yield better recognition and analysis results, we need to address two challenging issues of HSI, i.e., the existence of mixed pixels and its significantly low spatial resolution (LR). In this dissertation, spectral unmixing (SU) and hyperspectral image super-resolution (HSI-SR) approaches are developed to address these two issues with advanced deep learning models in an unsupervised fashion. A specific application, anomaly detection, is also studied, to show the importance of SU.Although deep learning has achieved the state-of-the-art performance on supervised problems, its practice on unsupervised problems has not been fully developed. To address the problem of SU, an untied denoising autoencoder is proposed to decompose the HSI into endmembers and abundances with non-negative and abundance sum-to-one constraints. The denoising capacity is incorporated into the network with a sparsity constraint to boost the performance of endmember extraction and abundance estimation.Moreover, the first attempt is made to solve the problem of HSI-SR using an unsupervised encoder-decoder architecture by fusing the LR HSI with the high-resolution multispectral image (MSI). The architecture is composed of two encoder-decoder networks, coupled through a shared decoder, to preserve the rich spectral information from the HSI network. It encourages the representations from both modalities to follow a sparse Dirichlet distribution which naturally incorporates the two physical constraints of HSI and MSI. And the angular difference between representations are minimized to reduce the spectral distortion.Finally, a novel detection algorithm is proposed through spectral unmixing and dictionary based low-rank decomposition, where the dictionary is constructed with mean-shift clustering and the coefficients of the dictionary is encouraged to be low-rank. Experimental evaluations show significant improvement on the performance of anomaly detection conducted on the abundances (through SU).The effectiveness of the proposed approaches has been evaluated thoroughly by extensive experiments, to achieve the state-of-the-art results
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