A data-driven approach to solving a 1D inverse scattering problem

In this paper, we extend a recently proposed approach for inverse scattering with Neumann boundary conditions [Druskin et al., Inverse Probl. 37, 075003 (2021)] to the 1D Schrödinger equation with impedance (Robin) boundary conditions. This method approaches inverse scattering in two steps: first, to extract a reduced order model (ROM) directly from the data and, subsequently, to extract the scattering potential from the ROM. We also propose a novel data-assimilation (DA) inversion method based on the ROM approach, thereby avoiding the need for a Lanczos-orthogonalization (LO) step. Furthermore, we present a detailed numerical study and A comparison of the accuracy and stability of the DA and LO methods

Retrospective Study of Midazolam Protocol for Prehospital Behavioral Emergencies

Introduction: Agitated patients in the prehospital setting pose challenges for both patient care and emergency medical services (EMS) provider safety. Midazolam is frequently used to control agitation in the emergency department setting; however, limited data exist in the prehospital setting. We describe our experience treating patients with midazolam for behavioral emergencies in a large urban EMS system. We hypothesized that using midazolam for acute agitation leads to improved clinical conditions without causing significant clinical deterioration.Methods: We performed a retrospective review of EMS patient care reports following implementation of a behavioral emergencies protocol in a large urban EMS system from February 2014–June 2016. For acute agitation, paramedics administered midazolam 1 milligram (mg) intravenous (IV), 5 mg intramuscular (IM), or 5 mg intranasal (IN). Results were analyzed using descriptive statistics, Levene’s test for assessing variance among study groups, and t-test to evaluate effectiveness based on route.Results: In total, midazolam was administered 294 times to 257 patients. Median age was 30 (interquartile range 24–42) years, and 66.5% were male. Doses administered were 1 mg (7.1%) and 5 mg (92.9%). Routes were IM (52.0%), IN (40.8%), and IV (7.1%). A second dose was administered to 37 patients. In the majority of administrations, midazolam improved the patient’s condition (73.5%) with infrequent adverse events (3.4%). There was no significant difference between the effectiveness of IM and IN midazolam (71.0% vs 75.4%; p = 0.24).Conclusion: A midazolam protocol for prehospital agitation was associated with reduced agitation and a low rate of adverse events

A data-driven approach to solving a 1D inverse scattering problem

In this paper, we extend a recently proposed approach for inverse scattering with Neumann boundary conditions [Druskin et al., Inverse Probl. 37, 075003 (2021)] to the 1D Schrödinger equation with impedance (Robin) boundary conditions. This method approaches inverse scattering in two steps: first, to extract a reduced order model (ROM) directly from the data and, subsequently, to extract the scattering potential from the ROM. We also propose a novel data-assimilation (DA) inversion method based on the ROM approach, thereby avoiding the need for a Lanczos-orthogonalization (LO) step. Furthermore, we present a detailed numerical study and A comparison of the accuracy and stability of the DA and LO methods

A regularised total least squares approach for 1D inverse scattering

We study the inverse scattering problem for a Schrödinger operator related to a static wave operator with variable velocity, using the GLM (Gelfand–Levitan–Marchenko) integral equation. We assume to have noisy scattering data, and we derive a stability estimate for the error of the solution of the GLM integral equation by showing the invertibility of the GLM operator between suitable function spaces. To regularise the problem, we formulate a variational total least squares problem, and we show that, under certain regularity assumptions, the optimisation problem admits minimisers. Finally, we compute numerically the regularised solution of the GLM equation using the total least squares method in a discrete sense

A distributional Gelfand–Levitan–Marchenko equation for the Helmholtz scattering problem on the line

We study an inverse scattering problem for the Helmholtz equation on the whole line. The goal of this paper is to obtain a Gelfand–Levitan–Marchenko (GLM)-type equation for the Jost solution that corresponds to the 1D Helmholtz differential operator. We assume for simplicity that the refraction index is of compact support. Using the asymptotic behavior of the Jost solutions with respect to the wave-number, we derive a generalized Povzner–Levitan representation in the space of tempered distributions. Then, we apply the Fourier transform on the scattering relation that describes the solutions of the Helmholtz scattering problem and we derive a generalized GLM equation. Finally, we discuss the possible application of this new generalized GLM equation to the inverse medium problem

Synergistic exploitation of geoinformation methods for post-earthquake 3D mapping of Vrisa traditional settlement, Lesvos Island, Greece

The aim of this paper is to present the methodology followed and the results obtained by the synergistic exploitation of geo-information methods towards 3D mapping of the impact of the catastrophic earthquake of June 12th 2017 on the traditional settlement of Vrisa on the island of Lesvos, Greece. A campaign took place for collecting: a) more than 150 ground control points using an RTK system, b) more than 20.000 high-resolution terrestrial and aerial images using cameras and Unmanned Aircraft Systems and c) 140 point clouds by a 3D Terrestrial Laser Scanner. The Structure from Motion method has been applied on the high-resolution terrestrial and aerial photographs, for producing accurate and very detailed 3D models of the damaged buildings of the Vrisa settlement. Additionally, two Orthophoto maps and Digital Surface Models have been created, with a spatial resolution of 5cm and 3cm, respectively. The first orthophoto map has been created just one day after the earthquake, while the second one, a month later. In parallel, 3D laser scanning data have been exploited in order to validate the accuracy of the 3D models and the RTK measurements used for the geo-registration of all the above-mentioned datasets. The significant advantages of the proposed methodology are: a) the coverage of large scale areas; b) the production of 3D models having very high spatial resolution and c) the support of post-earthquake management and reconstruction processes of the Vrisa village, since such 3D information can serve all stakeholders, be it national and/or local organizations

Gelfand-Levitan-Marchenko and model order reduction methods in inverse scattering

Inverse scattering problems arise in many applications, especially in imaging. In this thesis we studied frequency domain inverse scattering problems for the Helmholtz and the Schrödinger operators using both classical inverse scattering and modern reduced order model techniques. We started by revisiting the classical Gelfand-Levitan-Marchenko (GLM) integral equation method for solving the inverse Schrödinger scattering problem in 1D. The inverse Schrödinger scattering problem is interesting for imaging purposes, since it is possible to transform the Helmholtz and the (frequency domain) acoustic wave equation to the Schrödinger equation using a coordinate transform. In particular, we considered the GLM method with noise in the data, where we contributed an error bound for the solution of the unregularised GLM equation. We also proposed a regularised total least squares formulation in the infinite dimensional setting and we showed well posedness. Moreover, we studied the 1D scattering problem for the Helmholtz operator and we developed a GLM theory exclusively for the Helmholtz problem. In particular, we derived a generalised GLM equation in the space of tempered distributions for reconstructing the Jost solutions of the Helmholtz operator. To do so, we had to examine the asymptotic behaviour of the Jost solutions of the Helmholtz operator in terms of the wavenumber. After studying classical inverse scattering methods based on the GLM approach, we continued by studying inversion methods based on reduced order models (ROMs). We started with the inverse Schrödinger scattering problem of retrieving the scattering potential in 1D Schrödinger equation using boundary data. For that reason, we proposed a two-step approach inspired by a previously-published ROM-based method. We presented explicit expressions allowing the exact reconstruction of the ROM-matrices from boundary data and proposed a new data-assimilation approach for approximating the state from these matrices. Given the estimates of the states, the scattering potential is obtained by solving a Lippmann-Schwinger type integral equation. Finally, we combined the traditional FWI method with reduced order models and we proposed a new nonlinear inversion method for the inverse Helmholtz scattering problem. In particular, the input of our misfit functional consisted of the stiffness matrix of the ROM projection. In this case, we studied the well posedness of the nonlinear optimization problem and we derived the optimality condition. We finally compared numerically the ROM based FWI method with the conventional FWI method

Evolution of the settlements of Lesvos in the second half of the 20th century

The purpose of this doctoral thesis is to study the evolution of settlements, with a population of less than 2000 inhabitants, on the island of Lesvos, which is the study area, in the second half of the 20th century. This comparison is made based on three time points (1960, 1988, 1998) of the boundaries of settlements with a population of less than 2000 inhabitants, taking into account the aerial photographs of the H.M.G.S. of 1960, the boundaries established in these settlements with the P.D. 24-4 / 3-5-1984 D’ and the orthophoto maps of O.Η.Μ.C. year 1998. Most of these settlements pre-existed in 1923 and the definition of their boundaries is an important element for their development and evolution. To achieve this goal, GIS and Geoinformatics tools and techniques were used and the way in which they were used is analyzed in detail, in order to develop the methodology by which the questions posed were approached. To answer the questions, vector files of the borders were created at each time point, geographical databases, comparison tables, as well as maps for the visualization of the results. This doctoral study, which introduces innovative data in the recording, analysis and comparison of settlement development, can be a basis for future planning of their developmentΣκοπός της διδακτορικής αυτής εργασίας είναι να μελετήσει την εξέλιξη των οικισμών, με πληθυσμό μικρότερο από 2000 κατοίκους, στο νησί της Λέσβου, που αποτελεί τη περιοχή μελέτης, το 2ο μισό του 20ου αιώνα. Η σύγκριση αυτή πραγματοποιείται με βάση τρεις χρονικές στιγμές (1960, 1988, 1998) των ορίων των οικισμών με πληθυσμό μικρότερο από 2000 κατοίκους, λαμβάνοντας υπόψιν της αεροφωτογραφίες της ΓΥΣ του 1960, τα όρια που θεσπίστηκαν στους οικισμούς αυτούς με το Π.Δ. 24-4/3-5-1984 Δ΄ και τους ορθοφωτοχάρτες του Ο.Κ.Χ.Ε. του 1998. Οι περισσότεροι από τους οικισμούς αυτούς προϋπήρχαν του 1923 και ο καθορισμός των ορίων τους αποτελεί σημαντικό στοιχείο για την ανάπτυξη και την εξέλιξή τους. Για την επίτευξη του στόχου αυτού χρησιμοποιήθηκαν εργαλεία και τεχνικές ΣΓΠ και Γεωπληροφορικής και αναλύεται λεπτομερώς ο τρόπος με τον οποίο χρησιμοποιήθηκαν, για να αναπτυχθεί η μεθοδολογία με την οποία προσεγγίστηκαν τα ερωτήματα που ετέθησαν. Για την απάντηση των ερωτημάτων δημιουργήθηκαν διανυσματικά αρχεία των ορίων σε κάθε χρονική στιγμή, βάσεις γεωγραφικών δεδομένων, συγκριτικοί πίνακες, αλλά και χάρτες για την οπτικοποίηση των αποτελεσμάτων. Η διδακτορική μελέτη αυτή, που εισάγει καινοτόμα στοιχεία στην καταγραφή, την ανάλυση και την σύγκριση της εξέλιξης οικισμών, μπορεί να αποτελέσει βάση για τον μελλοντική σχεδιασμό της εξέλιξής τους