Multi- and hyper-spectral sensors generate a huge stream of data. A way around this problem is to use a compressive acquisition of the multi- and hyper-spectral object. The object is then reconstructed when needed. The next step is to avoid this reconstruction and to work directly with compressed data to achieve a conventional treatment on an object of this nature. After introducing a first approach using Riemannian tools to perform edge detection in multispectral image, we present the principles of the compressive sensing and algorithms used to solve its problems. Then we devote an entire chapter to the detailed study of one of them, Bregman type algorithms which by their flexibility and efficiency will allow us to solve the minimization encountered later. We then focuses on the detection of signatures in a multispectral image relying on an original algorithm of Guo and Osher based on minimizing $L_1$. This algorithm is generalized in connection with the acquisition compressed. A second generalization will help us to achieve the pattern detection in a multispectral image. And finally, we introduce new matrices of measures that greatly simplifies calculations while maintaining a good quality of measurements.
