Introduction to algorithms
Adaptive filter theory (2nd ed.)
Adaptive filter theory (2nd ed.)
Neural Networks for Optimization and Signal Processing
Neural Networks for Optimization and Signal Processing
The Linear l1 Estimator and the Huber M-Estimator
SIAM Journal on Optimization
Learning Overcomplete Representations
Neural Computation
A new regression estimator with neural network realization
IEEE Transactions on Signal Processing
An error-entropy minimization algorithm for supervised training ofnonlinear adaptive systems
IEEE Transactions on Signal Processing
System parameter estimation with input/output noisy data andmissing measurements
IEEE Transactions on Signal Processing
Performance analysis of minimum ℓ1-norm solutions for underdetermined source separation
IEEE Transactions on Signal Processing
Neural network for solving extended linear programming problems
IEEE Transactions on Neural Networks
Neural data fusion algorithms based on a linearly constrained least square method
IEEE Transactions on Neural Networks
A constructive algorithm for training cooperative neural network ensembles
IEEE Transactions on Neural Networks
A "nonnegative PCA" algorithm for independent component analysis
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
A compact cooperative recurrent neural network for computing general constrained L1norm estimators
IEEE Transactions on Signal Processing
CASE'09 Proceedings of the fifth annual IEEE international conference on Automation science and engineering
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The constrained L1 estimation is an attractive alternative to both the unconstrained L1 estimation and the least square estimation. In this letter, we propose a cooperative recurrent neural network (CRNN) for solving L1 estimation problems with general linear constraints. The proposed CRNN model combines four individual neural network models automatically and is suitable for parallel implementation. As a special case, the proposed CRNN includes two existing neural networks for solving unconstrained and constrained L1 estimation problems, respectively. Unlike existing neural networks, with penalty parameters, for solving the constrained L1 estimation problem, the proposed CRNN is guaranteed to converge globally to the exact optimal solution without any additional condition. Compared with conventional numerical algorithms, the proposed CRNN has a low computational complexity and can deal with the L1 estimation problem with degeneracy. Several applied examples show that the proposed CRNN can obtain more accurate estimates than several existing algorithms.