Electron tomography (ET) is a well-established technique for the 3D morphological characterization at the nanoscale. ET applied to spectroscopic modes for 3D structural and chemical analysis has become a hot topic but necessitates long exposure times and high beam currents. In this project, we will explore advanced compressed sensing (CS) approaches in order to improve the resolution of spectroscopic ET and reduce significantly the dose. More precisely, we will focus on the following two tasks: 1. Comparison of total variation minimization, orthogonal or undecimated wavelets, 3D curvelets or ridgelets and shearlets for nano-objects with different structures/textures; 2. Comparison of PCA and novel CS-inspired methods such as sparse PCA for dimensionality reduction and spectral un-mixing. The code will be written in Python, using Hyperspy (hyperspy.org) and PySAP (https://github.com/CEA-COSMIC/pysap) libraries. The project follows a multidisciplinary approach that involves the strong expertise of the coordinator in ET and the input of two collaborators with complementary skills: Philippe Ciuciu with expertise in MRI (DRF/Joliot/NEUROSPIN/Parietal) and Jean-Luc Starck with expertise in cosmology, signal processing and applied maths (DRF/IRFU/DAP/CosmoStat). The three communities share a strong interest in compressed sensing algorithms.