Improved image recovery from compressed data contaminated with impulsive noise

Area of Science:

• Signal Processing
• Information Theory
• Computational Imaging

Background:

• Compressed sensing (CS) enables data acquisition with sub-Nyquist sampling, crucial for applications like MRI and astronomy.
• Standard CS methods using the L2 norm on residuals are suboptimal for impulsive noise, potentially increasing recovery errors.
• Impulsive noise, common in real-world data, poses a challenge to the efficiency of traditional compressed sensing algorithms.

Discussion:

• This study introduces a robust compressed sensing formulation to mitigate the impact of impulsive noise by suppressing outliers in residuals.
• An iterative algorithm is proposed, leveraging existing compressed sensing solvers for efficient computation.
• The method demonstrates a reduced upper bound on recovery error for non-Gaussian noise distributions.

Key Insights:

• A novel robust formulation for compressed sensing is presented, specifically designed to handle impulsive noise.
• The proposed iterative algorithm effectively suppresses outliers, leading to more accurate data reconstruction.
• Numerical studies validate the method's efficacy in reducing recovery error under non-Gaussian noise conditions.

Outlook:

• The developed robust CS method offers improved performance in noisy imaging and data acquisition scenarios.
• Further research could explore extensions to different types of non-Gaussian noise and complex data structures.
• This work paves the way for more reliable and accurate compressed sensing applications in various scientific fields.