4D imaging in tomography and optical nanoscopy

Diese Dissertation gehört zu den Gebieten mathematische Bildverarbeitung und inverse Probleme. Ein inverses Problem ist die Aufgabe, Modellparameter anhand von gemessenen Daten zu berechnen. Solche Probleme treten in zahlreichen Anwendungen in Wissenschaft und Technik auf, z.B. in medizinischer Bildgebung, Biophysik oder Astronomie. Wir betrachten Rekonstruktionsprobleme mit Poisson Rauschen in der Tomographie und optischen Nanoskopie. Bei letzterer gilt es Bilder ausgehend von verzerrten und verrauschten Messungen zu rekonstruieren, wohingegen in der Positronen-Emissions-Tomographie die Aufgabe in der Visualisierung physiologischer Prozesse eines Patienten besteht. Standardmethoden zur 3D Bildrekonstruktion berücksichtigen keine zeitabhängigen Informationen oder Dynamik, z.B. Herzschlag oder Atmung in der Tomographie oder Zellmigration in der Mikroskopie. Diese Dissertation behandelt Modelle, Analyse und effiziente Algorithmen für 3D und 4D zeitabhängige inverse Probleme. This thesis contributes to the field of mathematical image processing and inverse problems. An inverse problem is a task, where the values of some model parameters must be computed from observed data. Such problems arise in a wide variety of applications in sciences and engineering, such as medical imaging, biophysics or astronomy. We mainly consider reconstruction problems with Poisson noise in tomography and optical nanoscopy. In the latter case, the task is to reconstruct images from blurred and noisy measurements, whereas in positron emission tomography the task is to visualize physiological processes of a patient. In 3D static image reconstruction standard methods do not incorporate time-dependent information or dynamics, e.g. heart beat or breathing in tomography or cell motion in microscopy. This thesis is a treatise on models, analysis and efficient algorithms to solve 3D and 4D time-dependent inverse problems

A framework for directional and higher-order reconstruction in photoacoustic tomography

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered back-projection, time reversal and least squares suffer from curved line artefacts and blurring, especially in the case of limited angles or strong noise. In recent years, there has been great interest in regularised iterative methods. These methods employ prior knowledge of the image to provide higher quality reconstructions. However, easy comparisons between regularisers and their properties are limited, since many tomography implementations heavily rely on the specific regulariser chosen. To overcome this bottleneck, we present a modular reconstruction framework for photoacoustic tomography, which enables easy comparisons between regularisers with different properties, e.g. nonlinear, higher-order or directional. We solve the underlying minimisation problem with an efficient first-order primal-dual algorithm. Convergence rates are optimised by choosing an operator-dependent preconditioning strategy. A variety of reconstruction methods are tested on challenging 2D synthetic and experimental data sets. They outperform direct reconstruction approaches for strong noise levels and limited angle measurements, offering immediate benefits in terms of acquisition time and quality. This work provides a basic platform for the investigation of future advanced regularisation methods in photoacoustic tomography

Risk estimators for choosing regularization parameters in ill-posed problems - Properties and limitations

This paper discusses the properties of certain risk estimators that recently regained popularity for choosing regularization parameters in ill-posed problems, in particular for sparsity regularization. They apply Stein’s unbiased risk estimator (SURE) to estimate the risk in either the space of the unknown variables or in the data space. We will call the latter PSURE in order to distinguish the two different risk functions. It seems intuitive that SURE is more appropriate for ill-posed problems, since the properties in the data space do not tell much about the quality of the reconstruction. We provide theoretical studies of both approaches for linear Tikhonov regularization in a finite dimensional setting and estimate the quality of the risk estimators, which also leads to asymptotic convergence results as the dimension of the problem tends to infinity. Unlike previous works which studied single realizations of image processing problems with a very low degree of ill-posedness, we are interested in the statistical behaviour of the risk estimators for increasing ill-posedness. Interestingly, our theoretical results indicate that the quality of the SURE risk can deteriorate asymptotically for ill-posed problems, which is confirmed by an extensive numerical study. The latter shows that in many cases the SURE estimator leads to extremely small regularization parameters, which obviously cannot stabilize the reconstruction. Similar but less severe issues with respect to robustness also appear for the PSURE estimator, which in comparison to the rather conservative discrepancy principle leads to the conclusion that regularization parameter choice based on unbiased risk estimation is not a reliable procedure for ill-posed problems. A similar numerical study for sparsity regularization demonstrates that the same issue appears in non-linear variational regularization approaches

Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity QED

Studies of ultracold atoms in optical lattices link various disciplines, providing a playground where fundamental quantum many-body concepts, formulated in condensed-matter physics, can be tested in much better controllable atomic systems, e.g., strongly correlated phases, quantum information processing. Standard methods to measure quantum properties of Bose-Einstein condensates (BECs) are based on matter-wave interference between atoms released from traps which destroys the system. Here we propose a nondestructive method based on optical measurements, and prove that atomic statistics can be mapped on transmission spectra of a high-Q cavity. This can be extremely useful for studying phase transitions between Mott insulator and superfluid states, since various phases show qualitatively distinct light scattering. Joining the paradigms of cavity quantum electrodynamics (QED) and ultracold gases will enable conceptually new investigations of both light and matter at ultimate quantum levels, which only recently became experimentally possible. Here we predict effects accessible in such novel setups.Comment: 6 pages, 3 figure

Secondary organic aerosol production from local emissions dominates the organic aerosol budget over Seoul, South Korea, during KORUS-AQ

Organic aerosol (OA) is an important fraction of submicron aerosols. However, it is challenging to predict and attribute the specific organic compounds and sources that lead to observed OA loadings, largely due to contributions from secondary production. This is especially true for megacities surrounded by numerous regional sources that create an OA background. Here, we utilize in situ gas and aerosol observations collected on board the NASA DC-8 during the NASA–NIER KORUS-AQ (Korea–United States Air Quality) campaign to investigate the sources and hydrocarbon precursors that led to the secondary OA (SOA) production observed over Seoul. First, we investigate the contribution of transported OA to total loadings observed over Seoul by using observations over the Yellow Sea coupled to FLEXPART Lagrangian simulations. During KORUS-AQ, the average OA loading advected into Seoul was ∼1–3 µg sm−3. Second, taking this background into account, the dilution-corrected SOA concentration observed over Seoul was ∼140 µgsm−3ppmv−1 at 0.5 equivalent photochemical days. This value is at the high end of what has been observed in other megacities around the world (20–70 µgsm−3ppmv−1 at 0.5 equivalent days). For the average OA concentration observed over Seoul (13 µg sm−3), it is clear that production of SOA from locally emitted precursors is the major source in the region. The importance of local SOA production was supported by the following observations. (1) FLEXPART source contribution calculations indicate any hydrocarbons with a lifetime of less than 1 day, which are shown to dominate the observed SOA production, mainly originate from South Korea. (2) SOA correlated strongly with other secondary photochemical species, including short-lived species (formaldehyde, peroxy acetyl nitrate, sum of acyl peroxy nitrates, dihydroxytoluene, and nitrate aerosol). (3) Results from an airborne oxidation flow reactor (OFR), flown for the first time, show a factor of 4.5 increase in potential SOA concentrations over Seoul versus over the Yellow Sea, a region where background air masses that are advected into Seoul can be measured. (4) Box model simulations reproduce SOA observed over Seoul within 11 % on average and suggest that short-lived hydrocarbons (i.e., xylenes, trimethylbenzenes, and semi-volatile and intermediate-volatility compounds) were the main SOA precursors over Seoul. Toluene alone contributes 9 % of the modeled SOA over Seoul. Finally, along with these results, we use the metric ΔOA/ΔCO2 to examine the amount of OA produced per fuel consumed in a megacity, which shows less variability across the world than ΔOA∕ΔCO

Airborne formaldehyde and volatile organic compound measurements over the Daesan petrochemical complex on Korea’s northwest coast during the Korea-United States Air Quality study

The U.S. National Aeronautics and Space Administration in partnership with Korea’s National Institute of Environmental Research embarked on the Korea-United States Air Quality (KORUS-AQ) study to address air quality issues over the Korean peninsula. Underestimation of volatile organic compound (VOC) emissions from various large facilities on South Korea’s northwest coast may contribute to this problem, and this study focuses on quantifying top-down emissions of formaldehyde (CH₂O) and VOCs from the largest of these facilities, the Daesan petrochemical complex, and comparisons with the latest emission inventories. To accomplish this and additional goals discussed herein, this study employed a number of measurements acquired during KORUS-AQ onboard the NASA DC-8 aircraft during three Daesan overflights on June 2, 3, and 5, 2016, in conjunction with a mass balance approach. The measurements included fast airborne measurements of CH₂O and ethane from an infrared spectrometer, additional fast measurements from other instruments, and a suite of 33 VOC measurements acquired by the whole air sampler. The mass balance approach resulted in consistent top-down yearly Daesan VOC emission flux estimates, which averaged (61 ± 14) × 10³ MT/year for the 33 VOC compounds, a factor of 2.9 ± 0.6 (±1.0) higher than the bottom-up inventory value. The top-down Daesan emission estimate for CH₂O and its four primary precursors averaged a factor of 4.3 ± 1.5 (± 1.9) times higher than the bottom-up inventory value. The uncertainty values in parentheses reflect upper limits for total uncertainty estimates. The resulting averaged top-down Daesan emission estimate for sulfur dioxide (SO₂) yielded a ratio of 0.81–1.0 times the bottom-up SO₂ inventory, and this provides an important cross-check on the accuracy of our mass balance analysis