Learning to Decode Cognitive States from Brain Images
Machine Learning
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Foundations of Computational Mathematics
Clustering with Bregman Divergences
The Journal of Machine Learning Research
Evaluation of Optimization Methods for Network Bottleneck Diagnosis
ICAC '07 Proceedings of the Fourth International Conference on Autonomic Computing
Blind source separation approach to performance diagnosis and dependency discovery
Proceedings of the 7th ACM SIGCOMM conference on Internet measurement
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Adaptive diagnosis in distributed systems
IEEE Transactions on Neural Networks
Compressed sensing performance bounds under Poisson noise
IEEE Transactions on Signal Processing
Discriminant sparse neighborhood preserving embedding for face recognition
Pattern Recognition
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
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The problem of sparse signal recovery from a relatively small number of noisy measurements has been studied extensively in the recent literature on compressed sensing. However, the focus of those studies appears to be limited to the case of linear projections disturbed by Gaussian noise, and the sparse signal reconstruction problem is treated as linear regression with l1-norm regularization constraint. A natural question to ask is whether one can accurately recover sparse signals under different noise assumptions. Herein, we extend the results of [13] to the more general case of exponential-family noise that includes Gaussian noise as a particular case, and yields l1-regularized Generalized Linear Model (GLM) regression problem. We show that, under standard restricted isometry property (RIP) assumptions on the design matrix, l1- minimization can provide stable recovery of a sparse signal in presence of the exponential-family noise, provided that certain sufficient conditions on the noise distribution are satisfied.