Learning Structured Compressed Sensing with Automatic Resource Allocation

Multidimensional data acquisition often requires extensive time and poses significant challenges for hardware and software regarding data storage and processing. Rather than designing a single compression matrix as in conventional compressed sensing, structured compressed sensing yields dimension-specific compression matrices, reducing the number of optimizable parameters. Recent advances in machine learning (ML) have enabled task-based supervised learning of subsampling matrices, albeit at the expense of complex downstream models. Additionally, the sampling resource allocation across dimensions is often determined in advance through heuristics. To address these challenges, we introduce Structured COmpressed Sensing with Automatic Resource Allocation (SCOSARA) with an information theory-based unsupervised learning strategy. SCOSARA adaptively distributes samples across sampling dimensions while maximizing Fisher information content. Using ultrasound localization as a case study, we compare SCOSARA to state-of-the-art ML-based and greedy search algorithms. Simulation results demonstrate that SCOSARA can produce high-quality subsampling matrices that achieve lower Cram\'er-Rao Bound values than the baselines. In addition, SCOSARA outperforms other ML-based algorithms in terms of the number of trainable parameters, computational complexity, and memory requirements while automatically choosing the number of samples per axis.

Misspecification of Multiple Scattering in Scalar Wave Fields and its Impact in Ultrasound Tomography

In this work, we investigate the localization of targets in the presence of multiple scattering. We focus on the often omitted scenario in which measurement data is affected by multiple scattering, and a simpler model is employed in the estimation. We study the impact of such model mismatch by means of the Misspecified Cram\'er-Rao Bound (MCRB). In numerical simulations inspired by tomographic inspection in ultrasound nondestructive testing, the MCRB is shown to correctly describe the estimation variance of localization parameters under misspecification of the wave propagation model. We provide extensive discussion on the utility of the MCRB in the practical task of verifying whether a chosen misspecified model is suitable for localization based on the properties of the maximum likelihood estimator and the nuanced distinction between bias and parameter space differences. Finally, we highlight that careful interpretation is needed whenever employing the classical CRB in the presence of mismatch through numerical examples based on the Born approximation and other simplified propagation models stemming from it.

Integrating AI in NDE: Techniques, Trends, and Further Directions

The digital transformation is fundamentally changing our industries, affecting planning, execution as well as monitoring of production processes in a wide range of application fields. With product line-ups becoming more and more versatile and diverse, the necessary inspection and monitoring sparks significant novel requirements on the corresponding Nondestructive Evaluation (NDE) systems. The establishment of increasingly powerful approaches to incorporate Artificial Intelligence (AI) may provide just the needed innovation to solve some of these challenges. In this paper we provide a comprehensive survey about the usage of AI methods in NDE in light of the recent innovations towards NDE 4.0. Since we cannot discuss each NDE modality in one paper, we limit our attention to magnetic methods, ultrasound, thermography, as well as optical inspection. In addition to reviewing recent AI developments in each field, we draw common connections by pointing out NDE-related tasks that have a common underlying mathematical problem and categorizing the state of the art according to the corresponding sub-tasks. In so doing, interdisciplinary connections are drawn that provide a more complete overall picture.

Efficient Convolutional Forward Modeling and Sparse Coding in Multichannel Imaging

This study considers the Block-Toeplitz structural properties inherent in traditional multichannel forward model matrices, using Full Matrix Capture (FMC) in ultrasonic testing as a case study. We propose an analytical convolutional forward model that transforms reflectivity maps into FMC data. Our findings demonstrate that the convolutional model excels over its matrix-based counterpart in terms of computational efficiency and storage requirements. This accelerated forward modeling approach holds significant potential for various inverse problems, notably enhancing Sparse Signal Recovery (SSR) within the context LASSO regression, which facilitates efficient Convolutional Sparse Coding (CSC) algorithms. Additionally, we explore the integration of Convolutional Neural Networks (CNNs) for the forward model, employing deep unfolding to implement the Learned Block Convolutional ISTA (BC-LISTA).