Interactive Analysis of Hyperspectral Data under Linearity Constraints

Large data sets delivered by imaging spectrometers are interesting in many ways in the Planetary Sciences. Due to the size of the data and lack of ground truth, which often prohibit conventional exploratory data analysis methods, interactive but unsupervised analysis methods could be a way of discovering relevant information about the sources that make up the data. In this work, we investigate some of the opportunities and limitations of such analyses based on non-negative matrix approximation in planetary settings. Since typically there often is no ground truth to compare to, the degrees of freedom inherent in the aforementioned approximation techniques often has to be constrained by users to discover physically valid sources and patterns. One way of going about this is to present users with different valid solutions have them choose the one or ones that fit their knowledge of the environment best. Recent developments have made it possible to exploit linear mixing constraints and present results to users in real or near-real time; thus, the approach has become practicable. The general setting of the problem is as follows: By considering P pixels of an hyperspectral image acquired at L frequency bands, the observed spectra are gathered in a PxL data matrix X. Each row of this matrix contains a measured spectrum at a pixel with spatial index p=1..P. According to the linear mixing model, the p-th spectrum, 1<=p<=P, can be expressed as a linear combination of r, 1<=r<=R, pure spectra of the surface components. Thus, X=AxS+E, E being an error matrix, should be minimised, where X, A, and S have only non-negative entries. The rows of matrix S now contain the pure surface spectra of the R components, and each entry of A corresponds to the abundance of the r-th component in pixel with spatial index p. For a qualitative and quantitative description of the observed scene composition, the estimation problem consists of finding matrices S and A which allow to explain the data matrix and, at the same time, have a coherent physical interpretation. This approach casts the hyperspectral unmixing as a source separation problem under a linear instantaneous mixing model. The implementation of the toolchain is based solely on open-source software, namely Scientific Python, along with a number of custom-written packages. The presentation will also cover the trade-offs that had been made when adapting the original batch-processing system to an interactive one, especially with cross-platform compatibility in mind, to keep differences between the systems to a minimum.