Mixtures of probabilistic principal component analyzers
Neural Computation
Learning Nonlinear Image Manifolds by Global Alignment of Local Linear Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Random Projections of Smooth Manifolds
Foundations of Computational Mathematics
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Modeling the manifolds of images of handwritten digits
IEEE Transactions on Neural Networks
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The compressive sensing theory shows that signals and images can be recovered from far fewer samples than that used in Shannon sampling theorem. In practical applications our aim is that an object should be meaningfully reconstructed in considerable detail relative to the full scene elsewhere at low sampling rate so that the target will be found directly from the reconstructed image. To achieve the goal, a new method based on manifold-based compressive sensing is proposed for object specific image reconstruction, in which the whole image is divided into small pieces and reconstructed piece by piece with the probability density function of the target as prior knowledge. Our reconstruction method is very fast since we divided the whole image into small pieces and the small pieces are reconstructed respectively. In our method, modeling a manifold of a target and getting the probability density function of the target is the key issue. And the model, which is used to obtain the probability density function about the target, is a Mixture of Factor Analyzers (MFA). The experiments results show that the target can be reconstructed more clearly than the full scene elsewhere at the low sampling rate with our method.