Determining the intrinsic dimension of a hyperspectral image using random matrix theory

Area of Science:

• Remote Sensing
• Signal Processing
• Data Science

Background:

• Accurate intrinsic dimension estimation is vital for hyperspectral image spectral unmixing.
• Under- or overestimation of intrinsic dimension leads to errors in unsupervised unmixing methods.
• Existing methods may require user-defined parameters or struggle with correlated noise.

Purpose of the Study:

• To develop a novel, unsupervised method for determining the intrinsic dimension of hyperspectral data.
• To leverage recent advances in random matrix theory for improved dimension estimation.
• To create a parameter-free method robust to spectrally correlated noise.

Main Methods:

• Application of random matrix theory to hyperspectral data.
• Unsupervised intrinsic dimension estimation.
• Robustness testing using synthetic data with varying noise characteristics and endmember spectral properties.

Main Results:

• The proposed method demonstrates robustness against noise levels, variability, and approximation.
• Successful dimension determination across various synthetic hyperspectral images.
• Validation on real-world hyperspectral datasets (Cuprite and Lunar Lakes) from AVIRIS, SpecTIR, and Hyperion sensors.

Conclusions:

• The novel random matrix theory-based method provides accurate and robust intrinsic dimension estimation for hyperspectral images.
• This unsupervised approach overcomes limitations of existing methods, particularly in handling noise.
• The method shows strong performance on both synthetic and real-world hyperspectral data, enhancing spectral unmixing.