Semi-realistic simulations of natural hyperspectral scenes

Many papers in the hyperspectral literature use simulations (based on a linear mixture model) to test algorithms, which either estimate the "intrinsic" dimensionality (ID) of the data or endmembers. Usually, these simulations use "real-world" endmembers, proportions distributed according to a uniform or Dirichlet distribution on the endmember simplex, and Gaussian errors which are "spectrally" and "spatially" uncorrelated. When the error standard deviations (SDs) in different bands are assumed to be unequal, they are usually estimated using Roger's method. The simulated and real-world data in these papers are so different that one cannot be confident that the various advocated methods work well with real-world data. We propose a general methodology which produces more realistic simulations, providing us with greater insights into the strengths and weaknesses of various advocated methods. With the aid of the well-known Indian Pines and Cuprite scenes, we compare several specific options within the proposed methodological framework. We also compare the performance of five well-known ID estimators using both real and simulated datasets and demonstrate that Roger's SD estimates are positively biased. A proof that Roger's estimates are always positively biased is given.