Component substitution and multiresolution analysis on hyperspectral microwave microscopy data sets

Scanning Microwave Microscopy (SMM) is a characterization method that uses a subwavelength probe tip to interact locally with a material and measure its complex electromagnetic properties. SMM scans the probe over a sample, mapping the complex reflection coefficient (S₁₁) pixel by pixel, together with information from an AFM that shares the same tip; both produce topographic and material-specific data. This data is shown as images. In hyperspectral SMM, data is acquired across multiple frequencies, often resulting in critical information distributed across several distinct images. To synthesize this data into a single, high-fidelity representation with all critical information available, this study evaluates three image fusion methods: Principal Component Analysis (PCA), Robust Principal Component Analysis (RPCA), and Discrete Wavelet Transform (DWT). To verify the algorithmic correctness of these fusion techniques, they are first applied to controlled synthetic datasets, where an idealized baseline for the combined features is established. The performance of these methods is quantified using standard image processing metrics, including Peak Signal-to-Noise Ratio (PSNR) and Root Mean Square Error (RMSE). Initial testing on synthetic datasets demonstrates that all three methods successfully integrate multi-frequency features. Quantitative evaluation indicates that while PCA achieves the highest PSNR for synthetic data, RPCA is the most effective for real SMM datasets, outperforming PCA by 4%-6% and DWT by 12%-99%. These results demonstrate RPCA's superior ability to consolidate hyperspectral information into a single comprehensive image despite its higher computational cost.