Iterative regularization for constrained minimization formulations of nonlinear inverse problems

In this paper we study the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type methods. We carry out a convergence analysis in the sense of regularization methods and discuss applicability to the problem of identifying the spatially varying diffusivity in an elliptic PDE from different sets of observations. Among these is a novel hybrid imaging technology known as impedance acoustic tomography, for which we provide numerical experiments.

Structural Stability of Urban Trees Using Visual and Instrumental Techniques: A Review

This review focuses on tree health assessment in urban forest, specifically on the methodologies commonly used to detect levels, dimensions, and location of wood deterioration. The acknowledged benefits to the urban forestry area from the application of assessment techniques are also addressed. A summary is presented of the different methodologies, such as visual analyses, acoustic tomography, and digital wood inspection drill, with the underlined importance of the biodeterioration of wood by fungi and termites.

Layer-Averaged Water Temperature Sensing in a Lake by Acoustic Tomography with a Focus on the Inversion Stratification Mechanism

Continuous sensing of water parameters is of great importance to fluid dynamic progress study in oceans, coastal areas and inland waters. The acoustic tomography technique can perform water temperature field measurements horizontally and vertically using sound wave travel information. The layer-averaged water temperature can also be measured with the acoustic tomography method. However, investigations focusing on the stratified mechanism, which consists of stratification form and its influence on inversion error, are seldom performed. In this study, an acoustic tomography experiment was carried out in a reservoir along two vertical slices to observe the layer-averaged water temperature. Specifically, multi-path sound travel information is identified through ray tracing using high-precision topography data obtained via a ship-mounted ADCP during the experiment. Vertical slices between sound stations are divided into different layers to study layer division inversion methods in different preset types. The inversion method is used to calculate the average water temperature and inversion temperature error of every layer. Different layer methods are studied with a comparison of results. The layer division principle studied in this paper can be used for layer-averaged water temperature sensing with multi-path sound transmission information.

Sustainable Management of Very Large Trees with the Use of Acoustic Tomography

This manuscript summarizes the process by which large trees are protected in Poland, how they gain protected status, and the use of acoustic tomography to assess the structural soundness of five individual trees. The authors discuss tree stressors and tree care options, and how the outcome of each assessment was used in the decision-making process. Moreover, the use of acoustic tomography as an assessment tool helps to gain public acceptance for the assessment. In sustainable development, there is talk of the conscious management of urban vegetation, and specifically tree populations in the city. In line with sustainable development, actions are taken to manage the existing natural resources, e.g., historic trees, properly. Thanks to using an acoustic tomograph, it is possible to diagnose old tree specimens, take care of the safety of people and property near the natural monument, and to test candidates for their eligibility as monuments. Thanks to the research presented, it was ordered that one poplar tree be left and observed in Lublin, that two linden trees be cut down in Sandomierz and Lublin, that arborist works consisting of lowering the height of a linden tree in Sandomierz be undertaken, and that monument protection be applied for an ash tree in Łęczna. A visual tree assessment (VTA) was the starting point for this research. Each of the trees could endanger the safety of site users, and the diagnostics performed using sound waves were crucial in assessing their health condition. Our results highlight that acoustic tomography is an essential diagnostic method applicable to trees belonging to cultural heritage, such as old trees, and is effective in preventive tree management through the monitoring of mid- to long-term changes in internal decay or cavities that are difficult to diagnose with the naked eye.

On the recovering of acoustic attenuation in 2D acoustic tomography

The inverse problem of recovering the acoustic attenuation in the inclusions inside the human tissue is considered. The coefficient inverse problem is formulated for the first-order system of PDE. We reduce the inverse problem to the optimization of the cost functional by gradient method. The gradient of the functional is determined by solving a direct and conjugate problem. Numerical results are presented.

Quantitative Evaluation of Bonded Silicon Wafer by Scanning Acoustic Tomography

In this paper, we report the results of a quantitative evaluation of the resolution and detectability on images obtained by SAT through silicon wafers with the thicknesses of 775 and 100 µm by transducers with the most appropriate focal length.

Monitoring of Yangtze River Discharge at Datong Hydrometric Station Using Acoustic Tomography Technology

To continuously monitor the discharge of the Yangtze River, two coastal acoustic tomography (CAT) systems with synchronized transmission were deployed at the Datong hydrometric station of the Yangtze River from July 2018 to January 2021. To accurately estimate the discharge of the Yangtze River, the cross-sectional averaged flow velocity and area data were estimated by establishing two empirical relationships: one between the range-averaged flow velocity measured by acoustic Doppler current profiler (ADCP) and the reciprocal travel time difference measured by CAT, and the other between the ADCP-measured cross-sectional area and the water-surface elevation (stage). Compared with the discharges directly measured by ADCP, our estimation had the root mean square error of 946 m3/s, accounting for 2.5% of the mean discharge. The discharges varied from 10,981 to 81,807 m3/s over the 2.5-years observational period, with a mean of 30,708 m3/s. The annual mean discharge was 29,163 and 34,763 m3/s in 2019 and 2020, respectively. Our monitoring successfully covered two complete flood processes, with a peak discharge of 69,744 (July 17, 2019) and 81,807 m3/s (July 13, 2020). Our study provides an innovative method to achieve accuracy and real-time monitoring of river discharges even during extreme flood events.