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Corrections to “Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds” [Dec 10 6140-6155]

Electr. & Comput. Eng. Dept., Duke Univ., Durham, NC, USA
IEEE Transactions on Signal Processing (Impact Factor: 2.79). 03/2011; 59(3):1329. DOI: 10.1109/TSP.2010.2070796
Source: DBLP

ABSTRACT

Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x ∈ RN that are of high dimension N but are constrained to reside in a low-dimensional subregion of RN. The number of mixture components and their rank are inferred automatically from the data. The resulting algorithm can be used for learning manifolds and for reconstructing signals from manifolds, based on compressive sensing (CS) projection measurements. The statistical CS inversion is performed analytically. We derive the required number of CS random measurements needed for successful reconstruction, based on easily-computed quantities, drawing on block-sparsity properties. The proposed methodology is validated on several synthetic and real datasets.

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    • "There are multiple reasons for adopting a GMM representation, which can be seen as a union of (linear or affine) subspaces, where each subspace is associated with the translation of the image of the (possibly low-rank) covariance matrix of each Gaussian component within the GMM. In fact, low-rank GMM priors have been shown to approximate signals in compact manifolds [11] and have been shown to provide state-of-the-art results in practical problems in image processing [12], dictionary learning [11], image classification [13] and video compression [14]. Of particular relevance, the adoption of GMM priors also offers an opportunity to analyze phase transitions in the classification "

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    • "However, FA is an unsupervised model, which seeks to explain the observations in terms of the extracted latent variables without using any label information [1] [2] [3]. In this case, we expect to develop a supervised latent model that utilizes FA to characterize the observation and meanwhile maximally exploit the predictive power of the label information. "
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    ABSTRACT: In this paper, we develop the max-margin similarity preserving factor analysis (MMSPFA) model. MMSPFA utilizes the latent variable support vector machine (LVSVM) as the classification criterion in the latent space to learn a discriminative subspace with max-margin constraint. It jointly learns factor analysis (FA) model, similarity preserving (SP) term and max-margin classifier in a united Bayesian framework to improve the prediction performance. Thanks to the conditionally conjugate property, the parameters in our model can be inferred via the simple and efficient Gibbs sampler. Finally, we test our methods on real-world data to demonstrate their efficiency and effectiveness.
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    • "This framework can be generalized to other applications and algorithms. For instance, Gaussian mixture model based dictionary learning approaches [49]–[53] that learn a union of subspaces can also benefit from side information. "
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    ABSTRACT: A blind compressive sensing algorithm is proposed to reconstruct hyperspectral images from spectrally-compressed measurements. The wavelength-dependent data are coded and then superposed, mapping the three-dimensional hyperspectral datacube to a two-dimensional image. The inversion algorithm learns a dictionary in situ from the measurements via globallocal shrinkage priors. By using RGB images as side information of the compressive sensing system, the proposed approach is extended to learn a coupled dictionary from the joint dataset of the compressed measurements and the corresponding RGB images, to improve reconstruction quality. A prototype camera is built using a liquid-crystal-on-silicon modulator. Experimental reconstructions of hyperspectral datacubes from both simulated and real compressed measurements demonstrate the efficacy of the proposed inversion algorithm, the feasibility of the camera and the benefit of side information.
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