Towards Gridless Sound Field Reconstruction

The sound field in a room can be represented by a weighted sum of room modes. To estimate the room modes, current literature uses on-the-grid, sparse reconstruction methods. However, these on-the-grid methods are known to suffer from basis mismatch. In this work, we investigate the use of a gridless framework for estimating room modes using atomic norm minimization, a gridless method. The advantage of this approach would be that it does not suffer from this basis mismatch problem. We derive a bound for the sound field reconstruction problem in a one-dimensional room with rigid walls and relate this to the frequency separation that is required by the atomic norm. We conclude that for perfect reconstruction based on the investigated gridless approach, additional prior knowledge about the signal model is required. We show how recovery is possible in a one-dimensional setting by exploiting both the structure of the sound field and the acquisition method.