Can one hear the shape of a room ? : Room geometry reconstruction from acoustic measurements using super-resolution and shape optimization

Overview & Synopsis

This thesis addresses the inverse problem of reconstructing the geometry of a room from acoustic measurements. Specifically, we focus on Room Impulse Responses. We develop two distinct approaches to tackle this problem. The first approach considers cuboid rooms with reflective walls and is based on the so-called Image Source Method. We propose a novel framework, utilizing the Frank-Wolfe algorithm, to reconstruct the 3D positions of image sources in a gridless manner by solving a convex optimization problem in the space of Radon measures. The second approach extends to more general room shapes. The inverse problem is formulated as a shape optimization problem, where the room geometry is refined by minimizing discrepancies between frequency-domain observations and the solution of the Helmholtz equation defined on the room domain.