On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and outlook on how to better use DL to improve the reliability and efficiency in PR. Furthermore, we present a live-updating resource (https://github.com/kqwang/phase-recovery) for readers to learn more about PR.Comment: 82 pages, 32 figure

Visualization and Localization of Interventional Devices with MRI by Susceptibility Mapping

Recently, interventional procedures can be performed with the visual assistance of MRI. However, the devices used in these procedures, such as brachytherapy seeds, biopsy needles, markers, and stents, have a large magnetic susceptibility that leads to severe signal loss and distortion in the MRI images and degrades the accuracy of the localization. Right now, there is no effective way to correctly identify, localize and visualize these interventional devices in MRI images. In this dissertation, we proposed a method to improve the accuracy of localization and visualization by generating positive contrast of the interventional devices using a regularized L1 minimization algorithm. Specifically, the spin-echo sequence with a shifted 180-degree pulse is used to acquire high SNR data. A short shift time is used to avoid severe phase wrap. A phase unwrapping method based on Markov Random Field using Highest-Confidence-First algorithm is proposed to unwrap the phase image. Then the phase images with different shifted time are used to calculate the field map. Next, L1 regularized deconvolution is performed to calculate the susceptibility map. With much higher susceptibility of the interventional devices than the background tissue, the interventional devices show positive-contrast in the susceptibility image. Computer simulations were performed to study the effect of the signal-to-noise ratio, resolution, orientation and size of the interventional devices on the accuracy of the results. Experiments were performed using gelatin and tissue phantom with brachytherapy seeds, gelatin phantoms with platinum wires, and water phantom with titanium needles. The results show that the proposed method provide positive contrast images of these interventional devices, differentiate them from other structures in the MRI images, and improves the visualization and localization of the devices

Innovative Techniques for the Retrieval of Earth’s Surface and Atmosphere Geophysical Parameters: Spaceborne Infrared/Microwave Combined Analyses

With the advent of the first satellites for Earth Observation: Landsat-1 in July 1972 and ERS-1 in May 1991, the discipline of environmental remote sensing has become, over time, increasingly fundamental for the study of phenomena characterizing the planet Earth. The goal of environmental remote sensing is to perform detailed analyses and to monitor the temporal evolution of different physical phenomena, exploiting the mechanisms of interaction between the objects that are present in an observed scene and the electromagnetic radiation detected by sensors, placed at a distance from the scene, operating at different frequencies. The analyzed physical phenomena are those related to climate change, weather forecasts, global ocean circulation, greenhouse gas profiling, earthquakes, volcanic eruptions, soil subsidence, and the effects of rapid urbanization processes. Generally, remote sensing sensors are of two primary types: active and passive. Active sensors use their own source of electromagnetic radiation to illuminate and analyze an area of interest. An active sensor emits radiation in the direction of the area to be investigated and then detects and measures the radiation that is backscattered from the objects contained in that area. Passive sensors, on the other hand, detect natural electromagnetic radiation (e.g., from the Sun in the visible band and the Earth in the infrared and microwave bands) emitted or reflected by the object contained in the observed scene. The scientific community has dedicated many resources to developing techniques to estimate, study and analyze Earth’s geophysical parameters. These techniques differ for active and passive sensors because they depend strictly on the type of the measured physical quantity. In my P.h.D. work, inversion techniques for estimating Earth’s surface and atmosphere geophysical parameters will be addressed, emphasizing methods based on machine learning (ML). In particular, the study of cloud microphysics and the characterization of Earth’s surface changes phenomenon are the critical points of this work

Kinematic models of interseismic deformation from inversion of GPS and InSAR measurements to estimate fault parameters and coupling degree

We have used kinematic models in two Italian regions to reproduce surface interseismic velocities obtained from InSAR and GPS measurements. We have considered a Block modeling, BM, approach to evaluate which fault system is actively accommodating the occurring deformation in both considered areas. We have performed a study for the Umbria-Marche Apennines, obtaining that the tectonic extension observed by GPS measurements is explained by the active contribution of at least two fault systems, one of which is the Alto Tiberina fault, ATF. We have estimated also the interseismic coupling distribution for the ATF using a 3D surface and the result shows an interesting correlation between the microseismicity and the uncoupled fault portions. The second area analyzed concerns the Gargano promontory for which we have used jointly the available InSAR and GPS velocities. Firstly we have attached the two datasets to the same terrestrial reference frame and then using a simple dislocation approach, we have estimated the best fault parameters reproducing the available data, providing a solution corresponding to the Mattinata fault. Subsequently we have considered within a BM analysis both GPS and InSAR datasets in order to evaluate if the Mattinata fault may accommodate the deformation occurring in the central Adriatic due to the relative motion between the North-Adriatic and South-Adriatic plates. We obtain that the deformation occurring in that region should be accommodated by more that one fault system, that is however difficult to detect since the poor coverage of geodetic measurement offshore of the Gargano promontory. Finally we have performed also the estimate of the interseismic coupling distribution for the Mattinata fault, obtaining a shallow coupling pattern. Both of coupling distributions found using the BM approach have been tested by means of resolution checkerboard tests and they demonstrate that the coupling patterns depend on the geodetic data positions

Physical-Mathematical modeling and numerical simulations of stress-strain state in seismic and volcanic regions

The strain-stress state generated by faulting or cracking and influenced by the strong heterogeneity of the internal earth structure precedes and accompanies volcanic and seismic activity. Particularly, volcanic eruptions are the culmination of long and complex geophysical processes and physical processes which involve the generation of magmas in the mantle or in the lower crust, its ascent to shallower levels, its storage and differentiation in shallow crustal chambers, and, finally, its eruption at the Earth’s surface. Instead, earthquakes are a frictional stick-slip instability arising along pre-existing faults within the brittle crust of the Earth. Long-term tectonic plate motion causes stress to accumulate around faults until the frictional strength of the fault is exceeded. The study of these processes has been traditionally carried out through different geological disciplines, such as petrology, structural geology, geochemistry or sedimentology. Nevertheless, during the last two decades, the development of physical of earth as well as the introduction of new powerful numerical techniques has progressively converted geophysics into a multidisciplinary science. Nowadays, scientists with very different background and expertises such as geologist, physicists, chemists, mathematicians and engineers work on geophysics. As any multidisciplinary field, it has been largely benefited from these collaborations. The different ways and procedures to face the study of volcanic and seismic phenomena do not exclude each other and should be regarded as complementary. Nowadays, numerical modeling in volcanology covers different pre-eruptive, eruptive and post-eruptive aspects of the general volcanic phenomena. Among these aspects, the pre-eruptive process, linked to the continuous monitoring, is of special interest because it contributes to evaluate the volcanic risk and it is crucial for hazard assessment, eruption prediction and risk mitigation at volcanic unrest. large faults. The knowledge of the actual activity state of these sites is not only an academic topic but it has crucial importance in terms of public security and eruption and earthquake forecast. However, numerical simulation of volcanic and seismic processes have been traditionally developed introducing several simplifications: homogeneous half-space, flat topography and elastic rheology. These simplified assumptions disregards effects caused by topography, presence of medium heterogeneity and anelastic rheology, while they could play an important role in Moreover, frictional sliding of a earthquake generates seismic waves that travel through the earth, causing major damage in places nearby to the modeling procedure This thesis presents mathematical modeling and numerical simulations of volcanic and seismic processes. The subject of major interest has been concerned on the developing of mathematical formulations to describe seismic and volcanic process. The interpretation of geophysical parameters requires numerical models and algorithms to define the optimal source parameters which justify observed variations. In this work we use the finite element method that allows the definition of real topography into the computational domain, medium heterogeneity inferred from seismic tomography study and the use of complex rheologies. Numerical forward method have been applied to obtain solutions of ground deformation expected during volcanic unrest and post-seismic phases, and an automated procedure for geodetic data inversion was proposed for evaluating slip distribution along surface rupture

Physical-Mathematical modeling and numerical simulations of stress-strain state in seismic and volcanic regions

The strain-stress state generated by faulting or cracking and influenced by the strong heterogeneity of the internal earth structure precedes and accompanies volcanic and seismic activity. Particularly, volcanic eruptions are the culmination of long and complex geophysical processes and physical processes which involve the generation of magmas in the mantle or in the lower crust, its ascent to shallower levels, its storage and differentiation in shallow crustal chambers, and, finally, its eruption at the Earth’s surface. Instead, earthquakes are a frictional stick-slip instability arising along pre-existing faults within the brittle crust of the Earth. Long-term tectonic plate motion causes stress to accumulate around faults until the frictional strength of the fault is exceeded. The study of these processes has been traditionally carried out through different geological disciplines, such as petrology, structural geology, geochemistry or sedimentology. Nevertheless, during the last two decades, the development of physical of earth as well as the introduction of new powerful numerical techniques has progressively converted geophysics into a multidisciplinary science. Nowadays, scientists with very different background and expertises such as geologist, physicists, chemists, mathematicians and engineers work on geophysics. As any multidisciplinary field, it has been largely benefited from these collaborations. The different ways and procedures to face the study of volcanic and seismic phenomena do not exclude each other and should be regarded as complementary. Nowadays, numerical modeling in volcanology covers different pre-eruptive, eruptive and post-eruptive aspects of the general volcanic phenomena. Among these aspects, the pre-eruptive process, linked to the continuous monitoring, is of special interest because it contributes to evaluate the volcanic risk and it is crucial for hazard assessment, eruption prediction and risk mitigation at volcanic unrest. large faults. The knowledge of the actual activity state of these sites is not only an academic topic but it has crucial importance in terms of public security and eruption and earthquake forecast. However, numerical simulation of volcanic and seismic processes have been traditionally developed introducing several simplifications: homogeneous half-space, flat topography and elastic rheology. These simplified assumptions disregards effects caused by topography, presence of medium heterogeneity and anelastic rheology, while they could play an important role in Moreover, frictional sliding of a earthquake generates seismic waves that travel through the earth, causing major damage in places nearby to the modeling procedure This thesis presents mathematical modeling and numerical simulations of volcanic and seismic processes. The subject of major interest has been concerned on the developing of mathematical formulations to describe seismic and volcanic process. The interpretation of geophysical parameters requires numerical models and algorithms to define the optimal source parameters which justify observed variations. In this work we use the finite element method that allows the definition of real topography into the computational domain, medium heterogeneity inferred from seismic tomography study and the use of complex rheologies. Numerical forward method have been applied to obtain solutions of ground deformation expected during volcanic unrest and post-seismic phases, and an automated procedure for geodetic data inversion was proposed for evaluating slip distribution along surface rupture

Magnetic Resonance Imaging of Susceptibility Effects in Carotid Atherosclerosis

This thesis explores the use of susceptibility-weighted imaging (SWI) and quantitative susceptibility mapping (QSM), to characterize carotid artery plaques with and without the use of ultrasmall superparamagnetic iron oxide (USPIO) nanoparticle contrast agents. The overall hypothesis is that QSM can serve to differentiate carotid artery plaque features of different susceptibility and provide a positive contrast mechanism for imaging the uptake of USPIOs. Chapter 1 describes the pathophysiology of carotid atherosclerosis. Vulnerable plaques, i.e. those at risk of rupture, can be characterized by the presence of a lipid rich necrotic core (LRNC), intraplaque haemorrhage (IPH), and inflammation. In addition, plaques may develop calcifications that may be protective of rupture. The chapter describes the established multi-contrast imaging protocols used for characterizing plaques. Furthermore, the use of USPIO-contrast agents to image inflammation is described. Chapter 2 describes the physical principles of MR image generation including the sensitivity to magnetic susceptibility. The principles of T2*w imaging, and susceptibility weighted imaging (SWI) are explained. Chapter 3 reviews the principles and post-processing steps involved in commonly used algorithms for QSM in terms of the underlying physical and mathematical principles which are then demonstrated in the form of numerical simulations. Chapter 4 presents the application of SWI to a group of patients who underwent USPIO enhanced MRI on a 1.5T MRI system. Images were acquired prior to infusion and 48 hours post infusion. SWI and gradient echo phase images were used to depict the field inhomogeneities generated by diamagnetic and paramagnetic materials within the plaques, calcification and USPIO-uptake. These results were then compared to a conventional carotid multi-contrast protocol, which includes R2*-mapping and T2*w imaging, and, where available, CT and histology. In chapter 5 QSM is performed in the carotid artery wall of a cohort of normal volunteers on a 1.5T MRI system. Unlike the brain, the neck contains fat which can cause severe errors in the field estimate, which propagate into the susceptibility map. Therefore, QSM was combined with water-fat separation for application in the neck to correct for these artifacts. This correctly estimated a high fat-fraction in fatty tissue in the neck and allowed for a detailed depiction of the anatomy of healthy volunteers. The susceptibility value measured in fatty tissue agreed with literature values. Chapter 6 applies QSM with water-fat separation to a subset of the patient group on a 1.5T MRI system. On pre-contrast scans QSM successfully identified calcification as diamagnetic tissue and the water-fat separation identified a lipid core. On the post-contrast susceptibility maps, USPIO-uptake was identified as hyperintense signal. This allows QSM to provide quantitative contrast in carotid imaging that can identify multiple features simultaneously and to simplify the imaging of USPIO-contrast. The results were confirmed using the multi-contrast carotid MRI protocol and, where available, histology and CT. Chapter 7 discusses the limitations of the current studies and the potential future improvements of the current methodology in terms of MR acquisition, post-processing algorithms and MR protocols. Future studies could serve to further evaluate the potential of QSM in carotid imaging and use it as a novel tool to quantify USPIO uptake in atherosclerotic carotid arteries

Optimising MRI Magnetic Susceptibility Mapping for Applications in Challenging Regions of the Body

Quantitative Susceptibility Mapping (QSM) is a recently developed Magnetic Resonance Imaging (MRI) technique that calculates the tissue magnetic susceptibility from MR phase images. While QSM is mostly used in brain images, it has great potential in other areas such as the head and neck where it has not yet been applied. Poorly oxygenated regions in head-and-neck tumours are expected to have a higher susceptibility due to the high concentration of paramagnetic deoxyhaemoglobin in the microvessels. Therefore, QSM could provide a non-invasive method for identifying hypoxic sites which are more resistant to radiation therapy. Therefore, the main goal of this work was to develop and optimise a QSM pipeline for the head-and-neck region. Applying the complicated processing procedure of QSM to this region is particularly challenging due to: ♦ unavoidable subject motion (e.g. swallowing), ♦ air-tissue interfaces inducing large background fields to be removed, ♦ and fatty tissue introducing an additional, chemical shift-induced phase component to the MRI signal. Moreover, as I have shown in the thesis, acquisition parameters such as image resolution and coverage of the region of interest have a substantial effect on measured susceptibilities. Therefore, tailoring the MRI acquisition is also crucial for accurate QSM in the head-and-neck region. I conducted a comprehensive optimisation of both the MRI acquisition and the QSM pipeline for head-and-neck images and addressed all the aforementioned problems. I developed and optimised a 6-minute acquisition protocol and a QSM processing pipeline. I also created a highly efficient phase unwrapping algorithm for challenging regions. Then, I showed that QSM, using the optimised protocol and pipeline, has high repeatability in the head and neck. Further, I applied this experience with a challenging region to clinical, pelvic MR images of the sacroiliac joint. I showed that bone marrow fat metaplasia has signi cantly higher susceptibility than normal bone marrow mainly due to its fat content