Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.

Persistence of ventilatory defect after resolution of pulmonary interstitial emphysema in a preterm baby

Pulmonary interstitial emphysema is a common complication of mechanical ventilation in preterm babies. We report a case of severe unilateral pulmonary interstitial emphysema in a premature newborn, treated with high-frequency oscillatory ventilation, lateral decubitus positioning and selective intubation. After complete radiological resolution of the pulmonary emphysema in the left lung, the patient was studied by electrical impedance tomography and a marked reduction of ventilation was identified in the left lung despite radiological resolution of the cysts. This finding indicates that functional abnormalities may persist for longer periods after radiologic resolution of such lesions.

Can heterogeneity in ventilation be good?

Selection of the optimal positive end-expiratory pressure (PEEP) to avoid ventilator-induced lung injury in patients under mechanical ventilation is still a matter of debate. Many methods are available, but none is considered the gold standard. In the previous issue of Critical Care, Zhao and colleagues applied a method based on electrical impedance tomography to help select the PEEP that minimized ventilation inhomogeneities. Though promising when alveolar collapse and overdistension are present, this method might be misleading in patients with normal lungs.

Pulmonary lesion induced by low and high positive end-expiratory pressure levels during protective ventilation in experimental acute lung injury

Objective: To investigate the effects of low and high levels of positive end-expiratory pressure (PEEP), without recruitment maneuvers, during lung protective ventilation in an experimental model of acute lung injury (ALI). Design: Prospective, randomized, and controlled experimental study. Setting: University research laboratory. Subjects: Wistar rats were randomly assigned to control (C) [saline (0.1 ml), intraperitoneally] and ALI [paraquat (15 mg/kg), intra peritoneally] groups. Measurements and Main Results: After 24 hours, each group was further randomized into four groups (six rats each) at different PEEP levels = 1.5, 3, 4.5, or 6 cm H(2)O and ventilated with a constant tidal volume (6 mL/kg) and open thorax. Lung mechanics [static elastance (Est, L) and viscoelastic pressure (Delta P2, L)] and arterial blood gases were measured before (Pre) and at the end of 1-hour mechanical ventilation (Post). Pulmonary histology (light and electron microscopy) and type III procollagen (PCIII) messenger RNA (mRNA) expression were measured after 1 hour of mechanical ventilation. In ALI group, low and high PEEP levels induced a greater percentage of increase in Est, L (44% and 50%) and Delta P2, L (56% and 36%) in Post values related to Pre. Low PEEP yielded alveolar collapse whereas high PEEP caused overdistension and atelectasis, with both levels worsening oxygenation and increasing PCIII mRNA expression. Conclusions: In the present nonrecruited ALI model, protective mechanical ventilation with lower and higher PEEP levels than required for better oxygenation increased Est, L and Delta P2, L, the amount of atelectasis, and PCIII mRNA expression. PEEP selection titrated for a minimum elastance and maximum oxygenation may prevent lung injury while deviation from these settings may be harmful. (Crit Care Med 2009; 37:1011-1017)

Aortic blood pressure measured via EIT: investigation of different measurement settings.

Electrical impedance tomography (EIT) allows the measurement of intra-thoracic impedance changes related to cardiovascular activity. As a safe and low-cost imaging modality, EIT is an appealing candidate for non-invasive and continuous haemodynamic monitoring. EIT has recently been shown to allow the assessment of aortic blood pressure via the estimation of the aortic pulse arrival time (PAT). However, finding the aortic signal within EIT image sequences is a challenging task: the signal has a small amplitude and is difficult to locate due to the small size of the aorta and the inherent low spatial resolution of EIT. In order to most reliably detect the aortic signal, our objective was to understand the effect of EIT measurement settings (electrode belt placement, reconstruction algorithm). This paper investigates the influence of three transversal belt placements and two commonly-used difference reconstruction algorithms (Gauss-Newton and GREIT) on the measurement of aortic signals in view of aortic blood pressure estimation via EIT. A magnetic resonance imaging based three-dimensional finite element model of the haemodynamic bio-impedance properties of the human thorax was created. Two simulation experiments were performed with the aim to (1) evaluate the timing error in aortic PAT estimation and (2) quantify the strength of the aortic signal in each pixel of the EIT image sequences. Both experiments reveal better performance for images reconstructed with Gauss-Newton (with a noise figure of 0.5 or above) and a belt placement at the height of the heart or higher. According to the noise-free scenarios simulated, the uncertainty in the analysis of the aortic EIT signal is expected to induce blood pressure errors of at least ± 1.4 mmHg.

Whither lung EIT: Where are we, where do we want to go and what do we need to get there?

Breathing moves volumes of electrically insulating air into and out of the lungs, producing conductivity changes which can be seen by electrical impedance tomography (EIT). It has thus been apparent, since the early days of EIT research, that imaging of ventilation could become a key clinical application of EIT. In this paper, we review the current state and future prospects for lung EIT, by a synthesis of the presentations of the authors at the 'special lung sessions' of the annual biomedical EIT conferences in 2009-2011. We argue that lung EIT research has arrived at an important transition. It is now clear that valid and reproducible physiological information is available from EIT lung images. We must now ask the question: How can these data be used to help improve patient outcomes? To answer this question, we develop a classification of possible clinical scenarios in which EIT could play an important role, and we identify clinical and experimental research programmes and engineering developments required to turn EIT into a clinically useful tool for lung monitoring.

Parallel modeling of the electric field distribution in the brain

The term "Brain Imaging" identi�es a set of techniques to analyze the structure and/or functional behavior of the brain in normal and/or pathological situations. These techniques are largely used in the study of brain activity. In addition to clinical usage, analysis of brain activity is gaining popularity in others recent �fields, i.e. Brain Computer Interfaces (BCI) and the study of cognitive processes. In this context, usage of classical solutions (e.g. f MRI, PET-CT) could be unfeasible, due to their low temporal resolution, high cost and limited portability. For these reasons alternative low cost techniques are object of research, typically based on simple recording hardware and on intensive data elaboration process. Typical examples are ElectroEncephaloGraphy (EEG) and Electrical Impedance Tomography (EIT), where electric potential at the patient's scalp is recorded by high impedance electrodes. In EEG potentials are directly generated from neuronal activity, while in EIT by the injection of small currents at the scalp. To retrieve meaningful insights on brain activity from measurements, EIT and EEG relies on detailed knowledge of the underlying electrical properties of the body. This is obtained from numerical models of the electric �field distribution therein. The inhomogeneous and anisotropic electric properties of human tissues make accurate modeling and simulation very challenging, leading to a tradeo�ff between physical accuracy and technical feasibility, which currently severely limits the capabilities of these techniques. Moreover elaboration of data recorded requires usage of regularization techniques computationally intensive, which influences the application with heavy temporal constraints (such as BCI). This work focuses on the parallel implementation of a work-flow for EEG and EIT data processing. The resulting software is accelerated using multi-core GPUs, in order to provide solution in reasonable times and address requirements of real-time BCI systems, without over-simplifying the complexity and accuracy of the head models.

Heterogeneous multicore systems for signal processing

This thesis explores the capabilities of heterogeneous multi-core systems, based on multiple Graphics Processing Units (GPUs) in a standard desktop framework. Multi-GPU accelerated desk side computers are an appealing alternative to other high performance computing (HPC) systems: being composed of commodity hardware components fabricated in large quantities, their price-performance ratio is unparalleled in the world of high performance computing. Essentially bringing “supercomputing to the masses”, this opens up new possibilities for application fields where investing in HPC resources had been considered unfeasible before. One of these is the field of bioelectrical imaging, a class of medical imaging technologies that occupy a low-cost niche next to million-dollar systems like functional Magnetic Resonance Imaging (fMRI). In the scope of this work, several computational challenges encountered in bioelectrical imaging are tackled with this new kind of computing resource, striving to help these methods approach their true potential. Specifically, the following main contributions were made: Firstly, a novel dual-GPU implementation of parallel triangular matrix inversion (TMI) is presented, addressing an crucial kernel in computation of multi-mesh head models of encephalographic (EEG) source localization. This includes not only a highly efficient implementation of the routine itself achieving excellent speedups versus an optimized CPU implementation, but also a novel GPU-friendly compressed storage scheme for triangular matrices. Secondly, a scalable multi-GPU solver for non-hermitian linear systems was implemented. It is integrated into a simulation environment for electrical impedance tomography (EIT) that requires frequent solution of complex systems with millions of unknowns, a task that this solution can perform within seconds. In terms of computational throughput, it outperforms not only an highly optimized multi-CPU reference, but related GPU-based work as well. Finally, a GPU-accelerated graphical EEG real-time source localization software was implemented. Thanks to acceleration, it can meet real-time requirements in unpreceeded anatomical detail running more complex localization algorithms. Additionally, a novel implementation to extract anatomical priors from static Magnetic Resonance (MR) scansions has been included.

Analog Signal Acquisition and Conditioning for Near-Field Capacitive Communication and Active Combined EEG-EIT Monitoring

The work of the present thesis is focused on the implementation of microelectronic voltage sensing devices, with the purpose of transmitting and extracting analog information between devices of different nature at short distances or upon contact. Initally, chip-to-chip communication has been studied, and circuitry for 3D capacitive coupling has been implemented. Such circuits allow the communication between dies fabricated in different technologies. Due to their novelty, they are not standardized and currently not supported by standard CAD tools. In order to overcome such burden, a novel approach for the characterization of such communicating links has been proposed. This results in shorter design times and increased accuracy. Communication between an integrated circuit (IC) and a probe card has been extensively studied as well. Today wafer probing is a costly test procedure with many drawbacks, which could be overcome by a different communication approach such as capacitive coupling. For this reason wireless wafer probing has been investigated as an alternative approach to standard on-contact wafer probing. Interfaces between integrated circuits and biological systems have also been investigated. Active electrodes for simultaneous electroencephalography (EEG) and electrical impedance tomography (EIT) have been implemented for the first time in a 0.35 um process. Number of wires has been minimized by sharing the analog outputs and supply on a single wire, thus implementing electrodes that require only 4 wires for their operation. Minimization of wires reduces the cable weight and thus limits the patient's discomfort. The physical channel for communication between an IC and a biological medium is represented by the electrode itself. As this is a very crucial point for biopotential acquisitions, large efforts have been carried in order to investigate the different electrode technologies and geometries and an electromagnetic model is presented in order to characterize the properties of the electrode to skin interface.

Influence of fluid and volume state on PaO(2) oscillations in mechanically ventilated pigs

ABSTRACT Varying pulmonary shunt fractions during the respiratory cycle cause oxygen oscillations during mechanical ventilation. In artificially damaged lungs, cyclical recruitment of atelectasis is responsible for varying shunt according to published evidence. We introduce a complimentary hypothesis that cyclically varying shunt in healthy lungs is caused by cyclical redistribution of pulmonary perfusion. Administration of crystalloid or colloid infusions would decrease oxygen oscillations if our hypothesis was right. Therefore, n = 14 mechanically ventilated healthy pigs were investigated in 2 groups: crystalloid (fluid) versus no-fluid administration. Additional volume interventions (colloid infusion, blood withdrawal) were carried out in each pig. Intra-aortal PaO(2) oscillations were recorded using fluorescence quenching technique. Phase shift of oxygen oscillations during altered inspiratory to expiratory (I:E) ventilation ratio and electrical impedance tomography (EIT) served as control methods to exclude that recruitment of atelectasis is responsible for oxygen oscillations. In hypovolemia relevant oxygen oscillations could be recorded. Fluid and volume state changed PaO(2) oscillations according to our hypothesis. Fluid administration led to a mean decline of 105.3 mmHg of the PaO(2) oscillations amplitude (P < 0.001). The difference of the amplitudes between colloid administration and blood withdrawal was 62.4 mmHg in pigs not having received fluids (P = 0.0059). Fluid and volume state also changed the oscillation phase during altered I:E ratio. EIT excluded changes of regional ventilation (i.e., recruitment of atelectasis) to be responsible for these oscillations. In healthy pigs, cyclical redistribution of pulmonary perfusion can explain the size of respiratory-dependent PaO(2) oscillations.

Influence of end-expiratory level and tidal volume on gravitational ventilation distribution during tidal breathing in healthy adults

Our understanding of regional filling of the lung and regional ventilation distribution is based on studies using stepwise inhalation of radiolabelled tracer gases, magnetic resonance imaging and positron emission tomography. We aimed to investigate whether these differences in ventilation distribution at different end-expiratory levels (EELs) and tidal volumes (V (T)s) held also true during tidal breathing. Electrical impedance tomography (EIT) measurements were performed in ten healthy adults in the right lateral position. Five different EELs with four different V (T)s at each EEL were tested in random order, resulting in 19 combinations. There were no measurements for the combination of the highest EEL/highest V (T). EEL and V (T) were controlled by visual feedback based on airflow. The fraction of ventilation directed to different slices of the lung (VENT(RL1)-VENT(RL8)) and the rate of the regional filling of each slice versus the total lung were analysed. With increasing EEL but normal tidal volume, ventilation was preferentially distributed to the dependent lung and the filling of the right and left lung was more homogeneous. With increasing V (T) and maintained normal EEL (FRC), ventilation was preferentially distributed to the dependent lung and regional filling became more inhomogeneous (p < 0.05). We could demonstrate that regional and temporal ventilation distribution during tidal breathing was highly influenced by EEL and V (T).

Regional and overall ventilation inhomogeneities in preterm and term-born infants

OBJECTIVES: We compared ventilation inhomogeneity assessed by electrical impedance tomography (EIT) and multiple breath washout (MBW) in preterm and term-born infants. We hypothesised that EIT measurements in spontaneously breathing infants are repeatable and that differences in regional ventilation distribution measured by EIT can distinguish between preterm and term-born infants. DESIGN: Cross-sectional group comparison study. SETTING: Lung function laboratory at a University Children's Hospital. PARTICIPANTS: Seventeen healthy term-born and 15 preterm infants at a matched postmenstrual age of 44 weeks. MEASUREMENTS AND RESULTS: We concurrently measured ventilation inhomogeneity by EIT, ventilation inhomogeneity (LCI) and functional residual capacity (FRC) by MBW and tidal breathing variables during unsedated quiet sleep. EIT measurements were highly repeatable (coefficient of variation 3.6%). Preterm infants showed significantly more ventilation of the independent parts of the lungs compared to healthy term-born infants assessed by EIT (mean difference 5.0, 95 CI 1.3-8%). Whereas the two groups showed no differences in lung volumes or ventilation inhomogeneities assessed by MBW, EIT discriminated better between term and preterm infants. (FRC/kg: mean difference 1.1 mL, 95% CI -1.4-3.8 mL; LCI: mean difference 0.03, 95% CI -0.32-0.25). CONCLUSIONS: EIT shows distinct differences in ventilation distribution between preterm and term-born infants, which cannot be detected by MBW. Although preterm infants are capable of dynamically maintaining overall functional residual volume and ventilation distribution, they show some spatial differences from fullterm infants.

Effect of different breathing AIDS on ventilation distribution in adults with cystic fibrosis.

BACKGROUND AND OBJECTIVES We investigated the effect of different breathing aids on ventilation distribution in healthy adults and subjects with cystic fibrosis (CF). METHODS In 11 healthy adults and 9 adults with CF electrical impedance tomography measurements were performed during spontaneous breathing, continuous positive airway pressure (CPAP) and positive expiratory pressure (PEP) therapy randomly applied in upright and lateral position. Spatial and temporal ventilation distribution was assessed. RESULTS The proportion of ventilation directed to the dependent lung significantly increased in lateral position compared to upright in healthy and CF. This effect was enhanced with CPAP but neutralised with PEP, whereas the effect of PEP was larger in the healthy group. Temporal ventilation distribution showed exactly the opposite with homogenisation during CPAP and increased inhomogeneity with PEP. CONCLUSIONS PEP shows distinct differences to CPAP with respect to its impact on ventilation distribution in healthy adults and CF subjects EIT might be used to individualise respiratory physiotherapy.

Effect of smoke inhalation on viscoelastic properties and ventilation distribution in sheep

Smoke inhalation injuries are the leading cause of mortality from burn injury. Airway obstruction due to mucus plugging and bronchoconstriction can cause severe ventilation inhomogeneity and worsen hypoxia. Studies describing changes of viscoelastic characteristics of the lung after smoke inhalation are missing. We present results of a new smoke inhalation device in sheep and describe pathophysiological changes after smoke exposure. Fifteen female Merino ewes were anesthetized and intubated. Baseline data using electrical impedance tomography and multiple-breath inert-gas washout were obtained by measuring ventilation distribution, functional residual capacity, lung clearance index, dynamic compliance, and stress index. Ten sheep were exposed to standardized cotton smoke insufflations and five sheep to sham smoke insufflations. Measured carboxyhemoglobin before inhalation was 3.87 +/- 0.28% and 5 min after smoke was 61.5 +/- 2.1%, range 50-69.4% ( P < 0.001). Two hours after smoke functional residual capacity decreased from 1,773 +/- 226 to 1,006 +/- 129 ml and lung clearance index increased from 10.4 +/- 0.4 to 14.2 +/- 0.9. Dynamic compliance decreased from 56.6 +/- 5.5 to 32.8 +/- 3.2 ml/ cmH(2)O. Stress index increased from 0.994 +/- 0.009 to 1.081 +/- 0.011 ( P < 0.01) ( all means +/- SE, P < 0.05). Electrical impedance tomography showed a shift of ventilation from the dependent to the independent lung after smoke exposure. No significant change was seen in the sham group. Smoke inhalation caused immediate onset in pulmonary dysfunction and significant ventilation inhomogeneity. The smoke inhalation device as presented may be useful for interventional studies.

VALIDATION OF A 'DISPLACEMENT TOMOGRAPHY' INVERSION METHOD FOR MODELING SHEET INTRUSIONS

The study of volcano deformation data can provide information on magma processes and help assess the potential for future eruptions. In employing inverse deformation modeling on these data, we attempt to characterize the geometry, location and volume/pressure change of a deformation source. Techniques currently used to model sheet intrusions (e.g., dikes and sills) often require significant a priori assumptions about source geometry and can require testing a large number of parameters. Moreover, surface deformations are a non-linear function of the source geometry and location. This requires the use of Monte Carlo inversion techniques which leads to long computation times. Recently, ‘displacement tomography’ models have been used to characterize magma reservoirs by inverting source deformation data for volume changes using a grid of point sources in the subsurface. The computations involved in these models are less intensive as no assumptions are made on the source geometry and location, and the relationship between the point sources and the surface deformation is linear. In this project, seeking a less computationally intensive technique for fracture sources, we tested if this displacement tomography method for reservoirs could be used for sheet intrusions. We began by simulating the opening of three synthetic dikes of known geometry and location using an established deformation model for fracture sources. We then sought to reproduce the displacements and volume changes undergone by the fractures using the sources employed in the tomography methodology. Results of this validation indicate the volumetric point sources are not appropriate for locating fracture sources, however they may provide useful qualitative information on volume changes occurring in the surrounding rock, and therefore indirectly indicate the source location.