Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Bayesian compressive sensing and projection optimization
Proceedings of the 24th international conference on Machine learning
Bayesian Inference and Optimal Design for the Sparse Linear Model
The Journal of Machine Learning Research
Optimized Projections for Compressed Sensing
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Bayesian Inference and Optimal Design for the Sparse Linear Model
The Journal of Machine Learning Research
Learning from measurements in exponential families
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Convex variational Bayesian inference for large scale generalized linear models
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
Informative sensing of natural images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Bayesian compressive sensing via belief propagation
IEEE Transactions on Signal Processing
Active learning and basis selection for kernel-based linear models: a Bayesian perspective
IEEE Transactions on Signal Processing
Bayesian compressive sensing using Laplace priors
IEEE Transactions on Image Processing
A hierarchical Bayesian model for frame representation
IEEE Transactions on Signal Processing
Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models
SIAM Journal on Imaging Sciences
Dimensionality reduction via compressive sensing
Pattern Recognition Letters
A Bayesian active learning framework for a two-class classification problem
MUSCLE'11 Proceedings of the 2011 international conference on Computational Intelligence for Multimedia Understanding
Gaussian Kullback-Leibler approximate inference
The Journal of Machine Learning Research
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We relate compressed sensing (CS) with Bayesian experimental design and provide a novel efficient approximate method for the latter, based on expectation propagation. In a large comparative study about linearly measuring natural images, we show that the simple standard heuristic of measuring wavelet coefficients top-down systematically outperforms CS methods using random measurements; the sequential projection optimisation approach of (Ji & Carin, 2007) performs even worse. We also show that our own approximate Bayesian method is able to learn measurement filters on full images efficiently which outperform the wavelet heuristic. To our knowledge, ours is the first successful attempt at "learning compressed sensing" for images of realistic size. In contrast to common CS methods, our framework is not restricted to sparse signals, but can readily be applied to other notions of signal complexity or noise models. We give concrete ideas how our method can be scaled up to large signal representations.