Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Non-linear modelling of microwave devices embedding nano-ferroelectric materials for real-time reconfigurable transmitarray

In this thesis work a nonlinear model for Interdigitated Capacitors (IDCs) based on ferroelectric materials, is proposed. Through the properties of materials such as Hafnium-Zirconium Oxide (HfZrO2), it is possible to realize tunable radiofrequency (RF) circuits. In particular, the model proposed in this thesis describes the use of an IDC, realized on a High-Resistivity silicon substrate, as a phase shifter for beam-steering applications. The model is obtained starting from already present experimental measurements, through which it is possible to identify a circuit model. The model is tested for both low power values and other power values using Harmonic Balance simulations, which show an excellent convergence of the model up to 40 dBm of input power. Furthermore, an array composed by two patches operating both at 2.55 GHz, which exploits the tunable properties of the HfZrO-based IDC is proposed. At 0dBm the model shows a 47° phase shift with polarization -1 V and 1 V which leads to a 11° steering of the main lobe of the array.

Synthetic generation of amyloid PET images by non-linear dimensionality reduction inversion

Privacy issues and data scarcity in PET field call for efficient methods to expand datasets via synthetic generation of new data that cannot be traced back to real patients and that are also realistic. In this thesis, machine learning techniques were applied to 1001 amyloid-beta PET images, which had undergone a diagnosis of Alzheimer’s disease: the evaluations were 540 positive, 457 negative and 4 unknown. Isomap algorithm was used as a manifold learning method to reduce the dimensions of the PET dataset; a numerical scale-free interpolation method was applied to invert the dimensionality reduction map. The interpolant was tested on the PET images via LOOCV, where the removed images were compared with the reconstructed ones with the mean SSIM index (MSSIM = 0.76 ± 0.06). The effectiveness of this measure is questioned, since it indicated slightly higher performance for a method of comparison using PCA (MSSIM = 0.79 ± 0.06), which gave clearly poor quality reconstructed images with respect to those recovered by the numerical inverse mapping. Ten synthetic PET images were generated and, after having been mixed with ten originals, were sent to a team of clinicians for the visual assessment of their realism; no significant agreements were found either between clinicians and the true image labels or among the clinicians, meaning that original and synthetic images were indistinguishable. The future perspective of this thesis points to the improvement of the amyloid-beta PET research field by increasing available data, overcoming the constraints of data acquisition and privacy issues. Potential improvements can be achieved via refinements of the manifold learning and the inverse mapping stages during the PET image analysis, by exploring different combinations in the choice of algorithm parameters and by applying other non-linear dimensionality reduction algorithms. A final prospect of this work is the search for new methods to assess image reconstruction quality.

Indoor and outdoor atmospheric fungal spores in the São Paulo metropolitan area (Brazil): species and numeric concentrations

The aim of this study was to estimate the indoor and outdoor concentrations of fungal spores in the Metropolitan Area of Sao Paulo (MASP), collected at different sites in winter/spring and summer seasons. The techniques adopted included cultivation (samples collected with impactors) and microscopic enumeration (samples collected with impingers). The overall results showed total concentrations of fungal spores as high as 36,000 per cubic meter, with a large proportion of non culturable spores (around 91 per cent of the total). Penicillium sp. and Aspergillus sp. were the dominant species both indoors and outdoors, in all seasons tested, occurring in more than 30 per cent of homes at very high concentrations of culturable airborne fungi [colony forming units(CFU) m−3]. There was no significant difference between indoor and outdoor concentrations. The total fungal spore concentration found in winter was 19 per cent higher than that in summer. Heat and humidity were the main factors affecting fungal growth; however, a non-linear response to these factors was found. Thus, temperatures below 16°C and above 25°C caused a reduction in the concentration (CFU m−3) of airborne fungi, which fits with MASP climatalogy. The same pattern was observed for humidity, although not as clearly as with temperature given the usual high relative humidity (above 70 per cent) in the study area. These results are relevant for public health interventions that aim to reduce respiratory morbidity among susceptible populations

Early, low-level auditory-somatosensory multisensory interactions impact reaction time speed.

Several lines of research have documented early-latency non-linear response interactions between audition and touch in humans and non-human primates. That these effects have been obtained under anesthesia, passive stimulation, as well as speeded reaction time tasks would suggest that some multisensory effects are not directly influencing behavioral outcome. We investigated whether the initial non-linear neural response interactions have a direct bearing on the speed of reaction times. Electrical neuroimaging analyses were applied to event-related potentials in response to auditory, somatosensory, or simultaneous auditory-somatosensory multisensory stimulation that were in turn averaged according to trials leading to fast and slow reaction times (using a median split of individual subject data for each experimental condition). Responses to multisensory stimulus pairs were contrasted with each unisensory response as well as summed responses from the constituent unisensory conditions. Behavioral analyses indicated that neural response interactions were only implicated in the case of trials producing fast reaction times, as evidenced by facilitation in excess of probability summation. In agreement, supra-additive non-linear neural response interactions between multisensory and the sum of the constituent unisensory stimuli were evident over the 40-84 ms post-stimulus period only when reaction times were fast, whereas subsequent effects (86-128 ms) were observed independently of reaction time speed. Distributed source estimations further revealed that these earlier effects followed from supra-additive modulation of activity within posterior superior temporal cortices. These results indicate the behavioral relevance of early multisensory phenomena.

Rainfall erosivity for the State of Rio de Janeiro estimated by artificial neural network

The Artificial Neural Networks (ANNs) are mathematical models method capable of estimating non-linear response plans. The advantage of these models is to present different responses of the statistical models. Thus, the objective of this study was to develop and to test ANNs for estimating rainfall erosivity index (EI30) as a function of the geographical location for the state of Rio de Janeiro, Brazil and generating a thematic visualization map. The characteristics of latitude, longitude e altitude using ANNs were acceptable to estimating EI30 and allowing visualization of the space variability of EI30. Thus, ANN is a potential option for the estimate of climatic variables in substitution to the traditional methods of interpolation.

Indoor and outdoor atmospheric fungal spores in the So Paulo metropolitan area (Brazil): species and numeric concentrations

The aim of this study was to estimate the indoor and outdoor concentrations of fungal spores in the Metropolitan Area of Sao Paulo (MASP), collected at different sites in winter/spring and summer seasons. The techniques adopted included cultivation (samples collected with impactors) and microscopic enumeration (samples collected with impingers). The overall results showed total concentrations of fungal spores as high as 36,000 per cubic meter, with a large proportion of non culturable spores (around 91% of the total). Penicillium sp. and Aspergillus sp. were the dominant species both indoors and outdoors, in all seasons tested, occurring in more than 30% of homes at very high concentrations of culturable airborne fungi [colony forming units(CFU) m(-3)]. There was no significant difference between indoor and outdoor concentrations. The total fungal spore concentration found in winter was 19% higher than that in summer. Heat and humidity were the main factors affecting fungal growth; however, a non-linear response to these factors was found. Thus, temperatures below 16A degrees C and above 25A degrees C caused a reduction in the concentration (CFU m(-3)) of airborne fungi, which fits with MASP climatalogy. The same pattern was observed for humidity, although not as clearly as with temperature given the usual high relative humidity (above 70%) in the study area. These results are relevant for public health interventions that aim to reduce respiratory morbidity among susceptible populations.

Uso da restrição alimentar quantitativa para diminuir a mortalidade de frangos de corte machos

The effect of feed restriction (0, 10, 20, 30, 40 and 50%) from 8 until 14 days post-hatching on performance, total mortality incidence and sudden death syndrome (SDS) rate was studied in male broilers during winter and summer.Ad libitum fed broilers had a better performance, but a higher total mortality rate (13.00% in winter, 3.67% in summer) and SDS (3.67% in winter, 0.67% in summer). All restricted groups had a lower mortality level in winter than the control group with a non linear response influenced by feed restriction. Birds submitted to 40% feed restriction showed the lowest mortality incidence (2.67%) followed by groups submitted to 30% (4.67%), 50% (5.33%) and 10% and 20% (7.67%) feed restriction. Birds fed ad libitum had the highest SDS incidence (3.67%, against .33, 1.00, .67, 1.33 and 1.33% at 10, 20, 30, 40, 50% feed restriction, respectively), but differences were not significant. In summer, incidences of total mortality and due to SDS were low and not influenced by feed restriction, either during the restrictive period itself (8 to 14 days) or during the total period of raising (1 to 49 days). In both seasons, the feed restricted birds showed compensatory gain only until three weeks post-restriction period. At 49 days, body weight and weight-gain were lower in feed restricted birds, but feed :gain ratio rate was improved. This resulted in better productivity index in winter, but not in summer. The feed restriction at 30 to 40% for seven days during the second week may decrease mortality in male broilers raised in winter without lowering productivity if the restriction is followed by at least three weeks of full feeding.

Geotechnical and structural behavior of the railroad track in large-scale apparatus

This paper analyses the static and dynamic behavior of the railroad track model in laboratory. Measurements of stresses and strains on a large-scale railroad track apparatus were studied. The model includes: compacted soil, representing the final layers of platform, ballast layer, and ties (steel, wooden, and pre-stressed concrete). The soil and soil ballast interface were instrumented with pneumatic stress gauge. Settlement measurement device were positioned at the same levels as the load cells. Loads were applied by hydraulic actuators, statically and dynamically. After the prescribed number of load cycles, in pre-determined intervals, stresses and strains were measured. Observations indicate that stress and strain distributions, transmitted by wooden or steel ties, behave similarly. A more favorable behavior was observed with pre-stressed concrete mono block ties. Non-linear response was observed after a threshold numbers of cycles were surpassed, showing that the strain modulus increases with the numbers of cycles. © 2009 IOS Press.

Nonlinear effects generation in suspended core chalcogenide fibre

In this work we report our achievements in the elaboration and optical characterizations of low-losses suspended core optical fibers elaborated from As2S3 glass. For preforms elaboration, alternatively to other processes like the stack and draw or extrusion, we use a process based on mechanical drilling. The drawing of these drilled performs into fibers allows reaching a suspended core geometry, in which a 2 μm diameter core is linked to the fiber clad region by three supporting struts. The different fibers that have been drawn show losses close to 0.9 dB/m at 1.55 μm. The suspended core waveguide geometry has also an efficient influence on the chromatic dispersion and allows its management. Indeed, the zero dispersion wavelength, which is around 5 μm in the bulk glass, is calculated to be shifted towards around 2μm in our suspended core fibers. In order to qualify their nonlinearity we have pumped them at 1.995 μm with the help of a fibered ns source. We have observed a strong non linear response with evidence of spontaneous Raman scattering and strong spectral broadening. © 2011 SPIE.

Computer simulations of slowly relaxing systems in external fields

Eine der offenen Fragen der aktuellen Physik ist das Verständnis von Systemen im Nichtgleichgewicht. Im Gegensatz zu der Gleichgewichtsphysik ist in diesem Bereich aktuell kein Formalismus bekannt der ein systematisches Beschreiben der unterschiedlichen Systeme ermöglicht. Um das Verständnis über diese Systeme zu vergrößern werden in dieser Arbeit zwei unterschiedliche Systeme studiert, die unter einem externen Feld ein starkes nichtlineares Verhalten zeigen. Hierbei handelt es sich zum einen um das Verhalten von Teilchen unter dem Einfluss einer extern angelegten Kraft und zum anderen um das Verhalten eines Systems in der Nähe des kritischen Punktes unter Scherung. Das Modellsystem in dem ersten Teil der Arbeit ist eine binäre Yukawa Mischung, die bei tiefen Temperaturen einen Glassübergang zeigt. Dies führt zu einer stark ansteigenden Relaxationszeit des Systems, so dass man auch bei kleinen Kräften relativ schnell ein nichtlineares Verhalten beobachtet. In Abhängigkeit der angelegten konstanten Kraft können in dieser Arbeit drei Regime, mit stark unterschiedlichem Teilchenverhalten, identifiziert werden. In dem zweiten Teil der Arbeit wird das Ising-Modell unter Scherung betrachtet. In der Nähe des kritischen Punkts kommt es in diesem Modell zu einer Beeinflussung der Fluktuationen in dem System durch das angelegte Scherfeld. Dies hat zur Folge, dass das System stark anisotrop wird und man zwei unterschiedliche Korrelationslängen vorfindet, die mit unterschiedlichen Exponenten divergieren. Infolgedessen lässt sich der normale isotrope Formalismus des "finite-size scaling" nicht mehr auf dieses System anwenden. In dieser Arbeit wird gezeigt, wie dieser auf den anisotropen Fall zu verallgemeinern ist und wie damit die kritischen Punkte, sowie die dazu gehörenden kritischen Exponenten berechnet werden können.

North-south palaeohydrological contrasts in the central Mediterranean during the Holocene: tentative synthesis and working hypotheses

On the basis of a multi-proxy approach and a strategy combining lacustrine and marine records along a north–south transect, data collected in the central Mediterranean within the framework of a collaborative project have led to reconstruction of high-resolution and well-dated palaeohydrological records and to assessment of their spatial and temporal coherency. Contrasting patterns of palaeohydrological changes have been evidenced in the central Mediterranean: south (north) of around 40° N of latitude, the middle part of the Holocene was characterised by lake-level maxima (minima), during an interval dated to ca. 10 300–4500 cal BP to the south and 9000–4500 cal BP to the north. Available data suggest that these contrasting palaeohydrological patterns operated throughout the Holocene, both on millennial and centennial scales. Regarding precipitation seasonality, maximum humidity in the central Mediterranean during the middle part of the Holocene was characterised by humid winters and dry summers north of ca. 40° N, and humid winters and summers south of ca. 40° N. This may explain an apparent conflict between palaeoclimatic records depending on the proxies used for reconstruction as well as the synchronous expansion of tree species taxa with contrasting climatic requirements. In addition, south of ca. 40° N, the first millennium of the Holocene was characterised by very dry climatic conditions not only in the eastern, but also in the central- and the western Mediterranean zones as reflected by low lake levels and delayed reforestation. These results suggest that, in addition to the influence of the Nile discharge reinforced by the African monsoon, the deposition of Sapropel 1 has been favoured (1) by an increase in winter precipitation in the northern Mediterranean borderlands, and (2) by an increase in winter and summer precipitation in the southern Mediterranean area. The climate reversal following the Holocene climate optimum appears to have been punctuated by two major climate changes around 7500 and 4500 cal BP. In the central Mediterranean, the Holocene palaeohydrological changes developed in response to a combination of orbital, ice-sheet and solar forcing factors. The maximum humidity interval in the south-central Mediterranean started ca. 10 300 cal BP, in correlation with the decline (1) of the possible blocking effects of the North Atlantic anticyclone linked to maximum insolation, and/or (2) of the influence of the remnant ice sheets and fresh water forcing in the North Atlantic Ocean. In the north-central Mediterranean, the lake-level minimum interval began only around 9000 cal BP when the Fennoscandian ice sheet disappeared and a prevailing positive NAO-(North Atlantic Oscillation) type circulation developed in the North Atlantic area. The major palaeohydrological oscillation around 4500–4000 cal BP may be a non-linear response to the gradual decrease in insolation, with additional key seasonal and interhemispheric changes. On a centennial scale, the successive climatic events which punctuated the entire Holocene in the central Mediterranean coincided with cooling events associated with deglacial outbursts in the North Atlantic area and decreases in solar activity during the interval 11 700–7000 cal BP, and to a possible combination of NAO-type circulation and solar forcing since ca. 7000 cal BP onwards. Thus, regarding the centennial-scale climatic oscillations, the Mediterranean Basin appears to have been strongly linked to the North Atlantic area and affected by solar activity over the entire Holocene. In addition to model experiments, a better understanding of forcing factors and past atmospheric circulation patterns behind the Holocene palaeohydrological changes in the Mediterranean area will require further investigation to establish additional high-resolution and well-dated records in selected locations around the Mediterranean Basin and in adjacent regions. Special attention should be paid to greater precision in the reconstruction, on millennial and centennial timescales, of changes in the latitudinal location of the limit between the northern and southern palaeohydrological Mediterranean sectors, depending on (1) the intensity and/or characteristics of climatic periods/oscillations (e.g. Holocene thermal maximum versus Neoglacial, as well as, for instance, the 8.2 ka event versus the 4 ka event or the Little Ice Age); and (2) on varying geographical conditions from the western to the eastern Mediterranean areas (longitudinal gradients). Finally, on the basis of projects using strategically located study sites, there is a need to explore possible influences of other general atmospheric circulation patterns than NAO, such as the East Atlantic–West Russian or North Sea–Caspian patterns, in explaining the apparent complexity of palaeoclimatic (palaeohydrological) Holocene records from the Mediterranean area.

Magnetic susceptibility, XRF and color reflectance data of DSDP Hole 72-516F, cores 113 and 114

Deep marine successions of early Campanian age from DSDP site 516F drilled at low paleolatitudes in the South Atlantic reveal distinct sub-Milankovitch variability in addition to precession and eccentricity related variations. Elemental abundance ratios point to a similar 5 climatic origin for these variations and exclude a quadripartite structure - as observed in the Mediterranean Neogene - of the precession related cycles as an explanation for the inferred semi-precession cyclicity in MS. However, the semi-precession cycle itself is likely an artifact, reflecting the first harmonic of the precession signal. The sub-Milankovitch variability is best approximated by a ~ 7 kyr cycle as shown by 10 spectral analysis and bandpass filtering. The presence of sub-Milankovitch cycles with a period similar to that of Heinrich events of the last glacial cycle is consistent with linking the latter to low-latitude climate change caused by a non-linear response to precession induced variations in insolation between the tropics.

A new modern analogue reference dataset and its application to the 430-kyr pollen record from Lake Biwa

This study presents a newly compiled dataset of modern pollen and climate data from 798 sites across Japan and the Russian Far East. This comprehensive reference dataset combined with the modern analogue technique (MAT) provides a powerful tool for pollen-based reconstruction of the Quaternary Northwest Pacific climate. Pollen-derived reconstruction of the modern climate at the reference pollen-sampling sites matches well with the estimated modern climate values (R2 values vary between 0.79 and 0.95, and RMSEP values vary between 5.8 and 9.7% of the modern climatic range for all nine tested variables). The successful testing of the method encourages its application to the fossil pollen records. We used a coarse-resolution pollen record from Lake Biwa to reconstruct glacial-interglacial climate dynamics in central Japan since ~438 kyr and compared it to the earlier reconstruction based on a less representative reference dataset. The current and earlier results consistently demonstrate that the coldest glacial intervals experienced pronounced cooling in winter and moderate cooling in summer, supporting the growth of cool mixed forest (COMX) where warm mixed forest (WAMX) predominates today. During the last glacial, maximum (~24 kyr BP) mean temperatures of the coldest (MTCO) and warmest (MTWA) month were about -13 °C (RMSEP = 2.34 °C) and 21 °C (RMSEP = 1.66 °C) respectively, and annual precipitation (PANN) was about 800 mm (RMSEP = 158.06 mm). During the thermal optimums of the interglacial intervals, the temperatures of the coldest and warmest month were above 0 °C and 25 °C respectively, leading to the reconstruction of WAMX and temperate conifer forest (TECO). Although both these vegetation types grow in the southern part of Japan today, WAMX requires warmer space. The presence of WAMX during marine isotope stages (MIS) 11 and 1, and its absence during MIS 9 and MIS 5 contradict the marine isotope and Antarctic ice records, suggesting that the latter two interglacials were the warmest of the last 800 kyr. The apparent contradiction allows at least three different explanations including low temporal resolution of the pollen record; different trends in CO2 concentrations during 'short' and 'long' interglacials; and regional climate variability and non-linear response of different regions to the global forcing. More definitive conclusions will be possible on the basis of forthcoming high-resolution pollen records from central Japan.

Microfossil cyclicity in Late Albian sediments of Kirchrode I borehole

We studied the biological response to orbital forcing in marine Upper Albian sediments recovered from the 245 m-long Kirchrode I borehole in the Lower Saxony basin in northwestern Germany. Results from quantitative analysis of planktonic and benthic foraminifera, of calcareous nannofossils, and radiolaria were used for this study. Spectral analysis in the depth domain indicates for the high sedimentation rate part of the Upper Albian dominant periods with wavelengths of 10±13 m, 5±6 m, and 2±3 m, which we interpret to represent the biological response to orbital forcing in the Milankovitch frequency bands eccentricity, obliquity, and precession, respectively. In addition, a low amplitude 40±50 m cycle was found, which would represent the long-term eccentricity variation of roughly 400 ka. Microfossil cyclicity does not change significantly within the whole core indicating sedimentation rates of 11±12 cm/ka on an average, with variations between 3.5 and 13 ka. Microfossils show greater variability in their abundance changes than the physical and chemical parameters and also greater power in the higher-frequency bands (obliquity and precession). While most of the planktonic foraminifer species studied are dominated by variations in the obliquity, most benthic foraminifer species show an additional strong influence of precession. These differences in the cyclicity of the abundance changes are interpreted as reflecting a stronger influence of low latitude water in the deep waters of the Late Albian Lower Saxony basin than in the shallow waters. This basin was part of a wide, 'Boreal' epicontinental sea, which was connected to the Tethys to the south via the Polish strait and via the Paris basin, and which was connected with the North Atlantic and Arctic to the north. In analogy to results from analysis of data from the Late Neogene, strong effects of precession interpreted as being more characteristic for changes/influences triggered in the low latitudes and those of obliquity to be more characteristic for influences from the high latitudes. The presence of a relatively strong eccentricity cycle, not only in the compound parameters, but also in the abundance changes of single species during the Late Albian means that there must have been a non-linear response to orbital forcing and internal feedbacks.