Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Compressed sensing of time-varying signals
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Online adaptive estimation of sparse signals: where RLS meets the l1-norm
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Learning bayesian network structure from massive datasets: the «sparse candidate« algorithm
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
On Kalman Filtering With Nonlinear Equality Constraints
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
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In the first part of this work, a novel Kalman filtering-based method is introduced for estimating the coefficients of sparse, or more broadly, compressible autoregressive models using fewer observations than normally required. By virtue of its (unscented) Kalman filter mechanism, the derived method essentially addresses the main difficulties attributed to the underlying estimation problem. In particular, it facilitates sequential processing of observations and is shown to attain a good recovery performance, particularly under substantial deviations from ideal conditions, those which are assumed to hold true by the theory of compressive sensing. In the remaining part of this paper we derive a few information-theoretic bounds pertaining to the problem at hand. The obtained bounds establish the relation between the complexity of the autoregressive process and the attainable estimation accuracy through the use of a novel measure of complexity. This measure is used in this work as a substitute to the generally incomputable restricted isometric property.