Efficient Tikhonov regularization parameter selection for multi-zone sound field reproduction

This study introduces two efficient methods for selecting Tikhonov regularization parameters in acoustical inverse problems. The first approach employs a binary search (BS) algorithm to identify the regularization parameter that satisfies a predefined power constraint. Compared to traditional iterative searches over N candidate values, BS reduces the number of iterations from N to log2N. The second method, Adaptive Normalized Tikhonov (ANT), combines the conventional L-curve and Normalized Tikhonov techniques. By fitting the ratio of the inverse system matrix’s largest eigenvalue to an exponential decay function during preprocessing at a few sample frequencies, ANT determines the regularization parameter with a single calculation for other frequencies. Both methods were experimentally validated in a multi-zone sound field reproduction scenario using a measured reverberant room impulse responses database. Results demonstrated that BS achieves a balance between reproduction accuracy and robustness while significantly improving efficiency. The ANT method provided the most stable system without iterative calculations. These improvements indicate that both approaches offer compelling solutions for real-time applications.