Negentropy-Based Sparsity-Promoting Reconstruction with Fast Iterative Solution from Noisy Measurements

Area of Science:

• Signal Processing
• Information Theory
• Optimization

Background:

• Compressed sensing enables sparse signal recovery from limited measurements.
• Real-world applications often involve complex, non-Gaussian noise, challenging standard reconstruction methods.
• Existing algorithms for noise-robust reconstruction can be computationally prohibitive.

Purpose of the Study:

• To develop a compressed sensing method robust to non-Gaussian noise.
• To improve the efficiency and adaptability of sparse signal reconstruction algorithms.
• To leverage maximum negentropy theory for enhanced noise resilience.

Main Methods:

• Formalized the problem as a constrained minimization problem.
• Utilized maximum negentropy theory for the objective function, incorporating a sparse L1-norm constraint.
• Developed an efficient algorithm based on the fast iterative shrinkage-thresholding algorithm (FISTA).

Main Results:

• The proposed method demonstrates enhanced robustness against complex noise.
• The developed algorithm exhibits faster convergence rates.
• Theoretical analysis and numerical experiments confirm superior accuracy and efficiency.

Conclusions:

• The negentropy-based compressed sensing approach effectively reconstructs sparse signals in the presence of non-Gaussian noise.
• The proposed efficient algorithm provides a practical solution for noise-robust sparse signal recovery.
• This work advances compressed sensing techniques for applications sensitive to complex noise environments.