Differentiable Max-Directivity Beamforming Normalization for Independent Vector Analysis

Independent vector analysis (IVA) minimizes an objective function to estimate separation filters that separate mixture signals into individual source signals. Unfortunately, IVA often suffers from the well-known block permutation problem. To mitigate that problem, the use of geometry knowledge has been studied, but two crucial issues remain: the necessity of non-differential processes outside the minimization and of high-level geometrical clues such as the directions of arrival (DOAs) of the source signals. This paper thus presents a novel IVA method whose objective function has a differentiable max-directivity beamforming normalization (MDBN) term. This term uses geometry knowledge from only a low-level geometrical clue (the positions of the microphone array) via the traditional beamforming (BF) concept that each separation filter should have a maximum gain for each specific DOA across all frequency bins. Thus, our overall objective function can be minimized by gradient descent, and the MDBN term encourages the separation filters to focus on specific directions, which implicitly estimates the most reasonable DOAs of the source signals at each iteration. Therefore, our method uses geometry knowledge while avoiding the above two issues and estimates good separation filters mitigating the permutation problem. Several experiments show that our method outperforms the conventional BF and IVA methods.