Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
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Proceedings of the 24th international conference on Machine learning
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Online dictionary learning for sparse coding
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Nonparametric factor analysis with beta process priors
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
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IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
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IEEE Transactions on Image Processing
A plurality of sparse representations is better than the sparsest one alone
IEEE Transactions on Information Theory
Infinite sparse factor analysis and infinite independent components analysis
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
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ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
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IEEE Transactions on Image Processing
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SIAM Journal on Optimization
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CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
Sparse Demixing of Hyperspectral Images
IEEE Transactions on Image Processing
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We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelength dependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. To achieve this objective, the imagery is divided into contiguous three-dimensional (3D) spatio-spectral blocks of spatial dimension much less than the image dimension. It is assumed that each such 3D block may be represented as a linear combination of dictionary elements of the same dimension, plus noise, and the dictionary elements are learned in situ based on the observed data (no a priori training). The number of dictionary elements needed for representation of any particular block is typically small relative to the block dimensions, and all the image blocks are processed jointly (“collaboratively") to infer the underlying dictionary. We address dictionary learning from a Bayesian perspective, considering two distinct means of imposing sparse dictionary usage. These models allow inference of the number of dictionary elements needed as well as the underlying wavelength-dependent noise statistics. It is demonstrated that drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements, yields significant advantages, relative to the more conventional approach of using an independent and identically distributed Gaussian prior for the dictionary elements; this advantage is particularly evident in the presence of noise. The framework is demonstrated by processing hyperspectral imagery with a significant number of voxels missing uniformly at random, with imagery at specific wavelengths missing entirely, and in the presence of substantial additive noise.