This study delves into acoustic inverse problems, where measured acoustic data is analyzed to estimate unknown properties of sound sources and fields. Such problems arise in diverse fields like audio engineering, environmental acoustics, and medical ultrasound. Tackling these challenges demands advanced mathematical and computational techniques due to the intricate nature of sound propagation and measurement uncertainties. The study primarily focuses on three key problems: developing a sparsity-based technique for near-field acoustic holography using compressive sensing, evaluating data-driven methods for near-field acoustic holography in reflective environments, and examining the performance of inverse algorithms in acoustic pyrometry.

The research introduces a novel approach called multipath orthogonal matching pursuit (MPOMP), which combines matching pursuit and orthogonal matching pursuit to enhance source localization in near-field acoustic holography. Compared to conventional methods like one norm convex optimization (L1CVX) and iteratively reweighted least squares (IRLS), MPOMP demonstrates superior source localization accuracy and significantly faster computational time.

In acoustically reflective environments, data-driven methods using machine learning models are explored to establish relationships between field weights and measured pressure. Linear regression with L-BFGS emerges as the most effective method, particularly for envirionments with low absorption coefficients.

Regarding acoustic pyrometry, which aims to non-intrusively measure temperature distributions in industrial settings, the study compares four regularization methods: Tikhonov, modified Tikhonov, Total Variation (TV), and Iterative Reweighted Least-Squares (IRLS). The modified Tikhonov method with sharp filter regularization outperforms the others, especially when using a coarse cell ratio.

Overall, this research contributes to advancing acoustic inverse problem-solving techniques, offering improved approaches for near-field acoustic holography, data-driven solutions in reflective environments, and temperature reconstruction in acoustic pyrometry applications.
The work has been published in the following journals:

https://doi.org/10.1121/10.0017115

https://doi.org/10.1016/j.measurement.2022.111356

https://doi.org/10.1016/j.apacoust.2021.108501​