Learning the model from the data

. The task of approximating data with a concise model comprising only a few parameters is a key concern in many applications, particularly in signal processing. These models, typically subspaces belonging to a specific class, are carefully chosen based on the data at hand. In this survey, we review the latest research on data approximation using models with few parameters, with a specific emphasis on scenarios where the data is situated in finite-dimensional vector spaces, functional spaces such as L 2 ( R d ), and other general situations. We highlight the invariant properties of these subspace-based models that make them suitable for diverse applications, particularly in the field of image processing.