Linh Viet Nguyen

Linh V. Nguyen, Markus Haltmeier

In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we thoroughly analyze in both the $L^2$- and $H^1$-settings. They are casted in the form of a nonstandard wave equation. We derive the well-pawedness of the aforementioned wave equation in a natural functional space, and also prove the finite speed of propagation. Under the uniqueness and visibility condition, our formulations of the standard iterative reconstruction methods, such as Landweber's and conjugate gradients (CG), achieve a linear rate of convergence in either $L^2$- or $H^1$-norm. When the visibility condition is not satisfied, the problem is severely ill-posed and one must apply a regularization technique to stabilize the solutions. To that end, we study two classes of regularization methods: (i) iterative, and (ii) variational regularization. In the case of full data, our simulations show that the CG method works best; it is very fast and robust. In the ill-posed case, the CG method behaves unstably. Total variation regularization method (TV), in this case, significantly improves the reconstruction quality.

Duy Nhat Phan, Sushant Jha, James P. Mavo et al.

Additive Manufacturing (AM) is transforming the manufacturing sector by enabling efficient production of intricately designed products and small-batch components. However, metal parts produced via AM can include flaws that cause inferior mechanical properties, including reduced fatigue response, yield strength, and fracture toughness. To address this issue, we leverage convolutional neural networks (CNN) to analyze thermal images of printed layers, automatically identifying anomalies that impact these properties. We also investigate various synthetic data generation techniques to address limited and imbalanced AM training data. Our models' defect detection capabilities were assessed using images of Nickel alloy 718 layers produced on a laser powder bed fusion AM machine and synthetic datasets with and without added noise. Our results show significant accuracy improvements with synthetic data, emphasizing the importance of expanding training sets for reliable defect detection. Specifically, Generative Adversarial Networks (GAN)-generated datasets streamlined data preparation by eliminating human intervention while maintaining high performance, thereby enhancing defect detection capabilities. Additionally, our denoising approach effectively improves image quality, ensuring reliable defect detection. Finally, our work integrates these models in the CLoud ADditive MAnufacturing (CLADMA) module, a user-friendly interface, to enhance their accessibility and practicality for AM applications. This integration supports broader adoption and practical implementation of advanced defect detection in AM processes.