An MM-Based Algorithm for ℓ1-Regularized Least-Squares Estimation With an Application to Ground Penetrating Radar...

Area of Science:

• Optimization Algorithms
• Signal Processing
• Machine Learning

Background:

• Least absolute shrinkage and selection operator (LASSO) is a powerful estimation method for high-dimensional data.
• Existing LASSO optimization methods can be computationally intensive.
• Ground penetrating radar (GPR) generates large datasets requiring efficient processing.

Purpose of the Study:

• To develop a novel algorithm for minimizing LASSO objective functions.
• To create an efficient extension of this algorithm for GPR image reconstruction.
• To evaluate the performance of the proposed algorithms against state-of-the-art methods.

Main Methods:

• The majorize-minimize method was employed to create the LASSO estimation via majorization-minimization (LMM) algorithm.
• An extension, the GPR-specific LMM (GPR-LMM), was formulated for GPR image reconstruction.
• Time and space complexity analyses were conducted for performance comparison.

Main Results:

• The LMM algorithm guarantees monotonic decrease in LASSO objective function values.
• The GPR-LMM algorithm demonstrates significant improvements in speed and memory efficiency compared to standard LMM.
• GPR-LMM outperforms competing algorithms in performance metrics for GPR data reconstruction.

Conclusions:

• The LMM algorithm provides a straightforward, parallelizable approach to LASSO optimization.
• The GPR-LMM algorithm is well-suited for handling the large datasets in GPR imaging.
• Both LMM and GPR-LMM show promising results in simulated and real GPR data reconstruction.