Atomic auto-encoders for learning sparse representations

At the Gretsi 2025, one session was about inverse problems. An example inverse problem involves find a high-dimensional signal \(x\) from low dimensional observations \(y\) under a linear model \(y = A x +z\) where \(z\) is a measurement noise, \(A\) the sensing matrix.

One approach involves compressed sensing where you try to decompose your signal as the combination of the smallest number of dictionnary elements. In this family of approachs, (Newson & Traonmilin, 2023) proposed latent auto-encoders.