Data-driven and physics-constrained acoustic holography based on optimizer unrolling

Nearfield Acoustic Holography (NAH) retrieves vibro-acoustic patterns of sound sources from non-contact measurements of sound in their proximity. NAH obtains images of structural vibrations to analyze the underlying acoustic phenomena. Holographic problems are typically ill-posed and yield infinitely many solutions. Unique solutions are obtained by optimizing a cost function that targets an approximate solution obeying the laws of physics while simultaneously satisfying constraints that represent prior knowledge characterizing the expected result. Which constraints to choose is highly critical for success, and yet the most challenging question to answer. Accuracy fluctuates with the quantity and the quality of these constraints and requires skillful formulation and tuning. Despite ongoing research on novel constraints and parameter tuning methods, as well as rapid advancements in Deep Learning, the state-of-the-art still exhibits substantial deficiencies. As the proposed solution, this article studies a Variational Network for NAH with the idea to fuse physical knowledge with data-driven modeling. The network retrieves the strengths of equivalent sources from measurements by unrolling an iterative optimizer, whose regularizing parameters are inferred via supervised learning. The proposed method outperforms established solvers in a comparative study, using both simulated and real-world data, and it generalizes well to unseen vibration patterns.