Nouvelles approches pour l’exploration des images hyperspectrales

Imaging techniques have made significant advances, allowing for detailed analysesof material composition and structural or morphological features. Among these,hyperspectral imaging (HSI) stands out as a powerful analytical tool, capturing a spectroscopic measurement for each pixel in an image. This generates high-dimensionaldata, presenting challenges in analysis, particularly in managing the interplay betweenspatial and spectral information. In unsupervised analyses, clustering and spectralunmixing methods are commonly used, but they face limitations in scenarios withintricate spatial structures, severe spectral overlap, and complex chemical compositions.Moreover, spatial-spectral correlation is often overlooked or poorly addressed.To face these issues, this thesis proposes a novel exploratory approach based on ageometric interpretation of normalized scores and loadings obtained from SingularValue Decomposition (SVD) analysis. The objective of this method is to extract themost essential information, in terms of linear mixture analysis, without the need foroptimization or complex calculations, particularly in scenarios with significant spectraland spatial overlap. The first main point of this thesis is to evaluate the advantagesand limitations of clustering and unmixing, establishing a domain of applicabilityof these methods in relation to the data structure. It also explores scenarios wherethe data structure deviates from ideal conditions for these techniques, leading tochallenges in effective analysis. Traditionally, hyperspectral data cube is unfoldedpixel-wise, converting the three-dimensional data into a two-dimensional matrix forchemometric analyses. While effective, this approach risks losing valuable spatial-spectralrelationships. The second main point of this thesis is the exploration oftensor-based decomposition techniques. Although tensor decomposition has beenwidely applied in chemometrics, its use in HSI remains limited. By treating the data asa third-order tensor, this approach preserves their structure, allowing for simultaneousanalysis of both spatial and spectral dimensions. This is particularly advantageousin complex cases where traditional methods struggle to capture the full informationcontent due to the overlooking of spatial-spectral relationships. The thesis thenintroduces an unsupervised approach for HSI analysis based on the rank-(Lr, Lr, 1)block term decomposition (BTD). This tensor-based method demonstrates its potential in handling complex cases where traditional techniques, which require the reshapeof the data cube, are inadequate. The proposed approaches were first evaluated onsimulated datasets to define their field of application. They were then applied tobenchmark hyperspectral datasets and real case studies, demonstrating their utilityin addressing complex spatial structures and significant spectral overlap across abroad range of applications. Overall, novel chemometric approaches that expand thepalette of exploratory tools for hyperspectral images analysis and improve samplecharacterization in complex analytical scenarios were developed.