Identifying linear combinations of ridge functions (Q1277211)

This paper is about an inverse problem. Let a given function \(f(\mathbf x)\) be some sum of ridge functions of the form \(\sum_{i=1}^mg_i(\mathbf a^i\cdot\mathbf x)\). We just know an upper bound on \(m\). We seek to identify the functions \(g_i\) and also to identify the directions \(\mathbf a^i\) from such limited information. Several ways to solve this nonlinear problem are discussed in this work.