Component substitution and multiresolution analysis on hyperspectral microwave microscopy data sets.

Area of Science:

• Materials Science
• Nanotechnology
• Electromagnetics

Background:

• Scanning Microwave Microscopy (SMM) characterizes materials by measuring electromagnetic properties using a probe tip.
• Hyperspectral SMM acquires data across multiple frequencies, resulting in distributed information across several images.
• Synthesizing this multi-frequency data into a single, high-fidelity image is crucial for comprehensive analysis.

Purpose of the Study:

• To evaluate and compare image fusion methods for hyperspectral SMM data.
• To determine the most effective method for consolidating multi-frequency SMM data into a single, comprehensive image.
• To assess the performance of Principal Component Analysis (PCA), Robust Principal Component Analysis (RPCA), and Discrete Wavelet Transform (DWT).

Main Methods:

• Application of PCA, RPCA, and DWT to synthetic and real SMM datasets.
• Quantitative performance evaluation using Peak Signal-to-Noise Ratio (PSNR) and Root Mean Square Error (RMSE).
• Verification of algorithmic correctness using controlled synthetic datasets with established baselines.

Main Results:

• All three fusion methods (PCA, RPCA, DWT) successfully integrated multi-frequency features in synthetic datasets.
• PCA achieved the highest PSNR on synthetic data.
• RPCA demonstrated superior performance on real SMM datasets, outperforming PCA by 4%-6% and DWT by 12%-99%.

Conclusions:

• RPCA is the most effective method for consolidating hyperspectral SMM data into a single comprehensive image.
• RPCA's superior performance on real data justifies its higher computational cost.
• This fusion approach enhances the analysis of complex material properties from hyperspectral SMM measurements.