Sparse signal reconstruction via recurrent neural networks with hyperbolic tangent function

Area of Science:

• Machine Learning
• Signal Processing
• Optimization

Background:

• L1-minimization is crucial for sparse signal reconstruction.
• Recurrent Neural Networks (RNNs) offer a promising approach for solving optimization problems.
• Existing RNNs for L1-minimization require further performance enhancements.

Purpose of the Study:

• To propose novel Recurrent Neural Networks (RNNs) for efficient L1-minimization.
• To introduce a Finite-Time RNN (FTRNN) by integrating sliding mode control.
• To validate the stability and convergence properties of the proposed models.

Main Methods:

• Design of a one-layer RNN using hyperbolic tangent function and projection matrix.
• Application of Lyapunov method to prove stability and global convergence of the RNN.
• Integration of sliding mode control into RNN to develop FTRNN with finite-time convergence.
• Experimental validation using sparse signal and image reconstruction.

Main Results:

• The proposed RNN demonstrates stability and global convergence.
• The FTRNN exhibits Lyapunov stability and finite-time convergence under Restricted Isometry Property (RIP) conditions.
• Comparative experiments show superior performance of the proposed RNN and FTRNN over existing methods.

Conclusions:

• The developed RNN and FTRNN are effective for L1-minimization problems.
• The FTRNN offers enhanced performance, particularly in sparse signal and image reconstruction.
• The proposed models represent a significant advancement in applying neural networks to L1-minimization challenges.