Performance evaluation of typical approximation algorithms for nonconvex ℓp-minimization in diffuse optical...

Area of Science:

• Medical Physics
• Biomedical Imaging
• Computational Science

Background:

• Sparse estimation methods, particularly those using the ℓp-norm (0
• These ℓp-norm regularizations introduce nonconvexity into the optimization function, necessitating the use of approximations for minimization.
• Understanding the performance of different approximation algorithms is key to advancing DOT image reconstruction.

Purpose of the Study:

• To systematically compare three common approximation methods for ℓp-norm minimization in DOT.
• To evaluate the efficacy of iteratively reweighted ℓ1-minimization (IRL1), iteratively reweighted least squares (IRLS), and iteratively thresholding method (ITM) for image reconstruction.
• To determine which method offers superior performance in terms of accuracy and shape recovery for DOT.

Main Methods:

• Implementation of IRL1, IRLS, and ITM algorithms for ℓp-norm minimization.
• Application of these methods to diffuse optical tomographic image reconstruction.
• Comparative analysis using three distinct numerical and gelatin phantom datasets.

Main Results:

• All three methods (IRL1, IRLS, ITM) produced comparable results in diffuse optical tomographic image reconstruction.
• Iteratively reweighted ℓ1-minimization (IRL1) demonstrated a marginal advantage in shape recovery.
• IRL1 also showed slightly better quantitative accuracy in the reconstructed DOT images across the tested phantoms.

Conclusions:

• The choice among IRL1, IRLS, and ITM for ℓp-norm minimization in DOT may have subtle impacts on reconstruction quality.
• IRL1 appears to be a slightly more robust method for achieving accurate shape and quantitative values in DOT imaging.
• Further investigation into these sparse estimation techniques could refine diffuse optical tomography applications.