Application of optimal transport and non-local methods to hyperspectral and multispectral image fusion

The world we live in is constantly under observation. Many areas such as offshore zones, deserts, agricultural land and cities are monitored. This monitoring is done throughout remote sensing satellites or cameras mounted on aircrafts. However, because of many technological and financial constraints, the development of imaging sensors with high accuracy is limited. Therefore, solutions such as multi-sensor data fusion overcome the different limitations an produce images with high quality. This thesis is about hyperspectral and multispectral image fusion. A hyperspectral image (HS) has a high spectral resolution and a low spatial resolution, whereas a multispectral image (MS) has a high spatial resolution and a low spectral resolution. The goal is the combination of the relevant information contained in each image into one final high resolution one. In this dissertation various methods for dealing with hyperspectral and multispectral image fusion are presented. The first part of the thesis uses tools from the optimal transport theory namely the regularized Wasserstein distances. The fusion problem is thus modeled as the minimization of the sum of two regularized Wasserstein distances. In the second part of this thesis, the hyperspectral and the multispectral fusion problem is presented differently. The latter is modeled as the minimization of four energy terms including a non-local term. Experiments were conducted on multiple datasets and the fusion was assessed visually and quantitatively for both fusion techniques. The performance of both models compares favorably with the state-of-the-art methods.