Discrete-Time Neural Network for Fast Solving Large Linear L1 Estimation Problems and Its Application to Image Restoration

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computat...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 23; no. 5; pp. 812 - 820
Main Authors: Xia, Youshen, Sun, Changyin, Zheng, Wei Xing
Format: Journal Article
Language:English
Published: New York, NY Institute of Electrical and Electronics Engineers 01.05.2012
Subjects:
Algorithms
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Computer Simulation
Connectionism. Neural networks
Exact sciences and technology
Image Interpretation, Computer-Assisted - methods
Linear Models
Neural Networks (Computer)
Nonlinear Dynamics
Pattern Recognition, Automated - methods
Pattern recognition. Digital image processing. Computational geometry
Signal Processing, Computer-Assisted
Image processing
Degenerate system
global convergence
Non gaussian noise
large linear L
Image restoration
Neural network
estimation problem
Optimal solution
Discrete time
Problem solving
Sparse representation
Robustness
Linear estimation
Discrete-time neural network
ISSN:2162-237X, 2162-2388, 2162-2388
Online Access:Get full text
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Summary:There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2012.2184800