ITC/USA 2014 Conference Proceedings / The Fiftieth Annual International Telemetering Conference and Technical Exhibition / October 20-23, 2014 / Town and Country Resort & Convention Center, San Diego, CA / Massive amounts of data are typically acquired in third generation full-waveform (FW) LIDAR systems to generate image-like depthmaps of a scene of acceptable quality. The sampling systems acquiring this data, however, seldom take into account the low information rate generally present in the FW signals and, consequently, they sample very inefficiently. Our main goal here is to compare two efficient sampling models and processes for the individual time-resolved FW signals collected by a LIDAR system. Specifically, we compare two approaches of sub-Nyquist sampling of the continuous-time LIDAR FW return pulses: (i) modeling FW signals as short-duration pulses with multiple bandlimited echoes, and (ii) modeling them as signals with finite rates of innovation (FRI).

Sampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified Pal´ Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter, we introduce a new interpolation process, the modified Pal interpolation, based on papers by P ´ al, J ´ oo´ and Szabo, and we establish the existence and uniqueness of interpolation polynomials of modified ´ Pal type. ´ The paradigm to recover signals with finite rate of innovation from their samples is a fairly recent field of study. In the second chapter, we show that causal bilevel signals with finite rate of innovation can be stably recovered from their samples provided that the sampling period is at or above the maximal local rate of innovation, and that the sampling kernel is causal and positive on the first sampling period. Numerical simulations are presented to discuss the recovery of bilevel causal signals in the presence of noise.

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The Shannon sampling framework is widely used for discrete representation of analog bandlimited signals, starting from samples taken at the Nyquist rate. In many practical applications, signals are not bandlimited. In order to accommodate such signals within the Shannon-Nyquist framework, one typically passes the signal through an anti-aliasing filter, which essentially performs bandlimiting. In applications such as RADAR, SONAR, ultrasound imaging, optical coherence to-mography, multiband signal communication, wideband spectrum sensing, etc., the signals to be sampled have a certain structure, which could manifest in one of the following forms: (i) sparsity or parsimony in a certain bases; (ii) shift-invariant representation; (iii) multi-band spectrum; (iv) finite rate of innovation property, etc.. By using such structure as a prior, one could devise efficient sampling strategies that operate at sub-Nyquist rates. In this Ph.D. thesis, we consider the problem of sampling and reconstruction of finite-rate-of-innovation (FRI) signals, which fall in one of the two classes: (i) Sum-of-weighted and time-shifted (SWTS) pulses; and (ii) Sum-of-weighted exponential (SWE). Finite-rate-of-innovation signals are not necessarily bandlimited, but they are specified by a finite number of free parameters per unit time interval. Hence, the FRI reconstruction problem could be solved by estimating the parameters starting from measurements on the signal. Typically, parameter estimation is done using high-resolution spectral estimation (HRSE) techniques such as the annihilating filter, matrix pencil method, estimation of signal parameter via rotational invariance technique (ESPRIT), etc.. The sampling issues include design of the sampling kernel and choice of the sampling grid structure. Following a frequency-domain reconstruction approach, we propose a novel technique to design compactly supported sampling kernels. The key idea is to cancel aliasing at certain set of uniformly spaced frequencies and make sure that the rest of the frequency response is specified such that the kernel follows the Paley-Wiener criterion for compactly supported functions. To assess the robustness in the presence of noise, we consider a particular class of the proposed kernel whose impulse response has the form of sum of modulated splines (SMS). In the presence of continuous-time and digital noise cases, we show that the reconstruction accuracy is improved by 5 to 25 dB by using the SMS kernel compared with the state-of-the-art compactly supported kernels. Apart from noise robustness, the SMS kernel also has polynomial-exponential reproducing property where the exponents are harmonically related. An interesting feature of the SMS kernel, in contrast with E-splines, is that its support is independent of the number of exponentials. In a typical SWTS signal reconstruction mechanism, first, the SWTS signal is trans formed to a SWE signal followed by uniform sampling, and then discrete-domain annihilation is applied for parameter estimation. In this thesis, we develop a continuous-time annihilation approach using the shift operator for estimating the parameters of SWE signals. Instead of using uniform sampling-based HRSE techniques, operator-based annihilation allows us to estimate parameters from structured non-uniform samples (SNS), and gives more accurate parameters estimates. On the application front, we first consider the problem of curve fitting and curve completion, specifically, ellipse fitting to uniform or non-uniform samples. In general, the ellipse fitting problem is solved by minimizing distance metrics such as the algebraic distance, geometric distance, etc.. It is known that when the samples are measured from an incomplete ellipse, such fitting techniques tend to estimate biased ellipse parameters and the estimated ellipses are relatively smaller than the ground truth. By taking into account the FRI property of an ellipse, we show how accurate ellipse fitting can be performed even to data measured from a partial ellipse. Our fitting technique first estimates the underlying sampling rate using annihilating filter and then carries out least-squares regression to estimate the ellipse parameters. The estimated ellipses have lesser bias compared with the state-of-the-art methods and the mean-squared error is lesser by about 2 to 10 dB. We show applications of ellipse fitting in iris images starting from partial edge contours. We found that the proposed method is able to localize iris/pupil more accurately compared with conventional methods. In a related application, we demonstrate curve completion to partial ellipses drawn on a touch-screen tablet. We also applied the FRI principle to imaging applications such as frequency-domain optical-coherence tomography (FDOCT) and nuclear magnetic resonance (NMR) spectroscopy. In these applications, the resolution is limited by the uncertainty principle, which, in turn, is limited by the number of measurements. By establishing the FRI property of the measurements, we show that one could attain super-resolved tomograms and NMR spectra by using the same or lesser number of samples compared with the classical Fourier-based techniques. In the case of FDOCT, by assuming a piecewise-constant refractive index of the specimen, we show that the measurements have SWE form. We show how super-resolved tomograms could be achieved using SNS-based reconstruction technique. To demonstrate clinical relevance, we consider FDOCT measurements obtained from the retinal pigment epithelium (RPE) and photoreceptor inner/outer segments (IS/OS) of the retina. We show that the proposed method is able to resolve the RPE and IS/OS layers by using only 40% of the available samples. In the context of NMR spectroscopy, the measured signal or free induction decay (FID) can be modelled as a SWE signal. Due to the exponential decay, the FIDs are non-stationary. Hence, one cannot directly apply autocorrelation-based methods such as ESPRIT. We develop DEESPRIT, a counterpart of ESPRIT for decaying exponentials. We consider FID measurements taken from amino acid mixture and show that the proposed method is able to resolve two closely spaced frequencies by using only 40% of the measurements. In summary, this thesis focuses on various aspects of sub-Nyquist sampling and demonstrates concrete applications to super-resolution imaging.

A low-order discrete dynamical system (DDS) for finite-rate chemistry of H2-air combustion is derived in 3D. Fourier series with a single wavevector are employed to represent dependent variables of subgrid-scale (SGS) behaviors for applications to large-eddy simulation (LES). A Galerkin approximation is applied to the governing equations for comprising the DDS. Regime maps are employed to aid qualitative determination of useful values for bifurcation parameters of the DDS. Both isotropic and anisotropic assumptions are employed when constructing regime maps and studying bifurcation parameters sequences. For H2-air reactions, two reduced chemical mechanisms are studied via the DDS. As input to the DDS, physical quantities from experimental turbulent flow are used. Numerical solutions consisting of time series of velocities, species mass fractions, temperature, and the sum of mass fractions are analyzed. Numerical solutions are compared with experimental data at selected spatial locations within the experimental flame to check whether this model is suitable for an entire flame field. The comparisons show the DDS can mimic turbulent combustion behaviors in a qualitative sense, and the time-averaged computed results of some species are quantitatively close to experimental data.

In many practical imaging scenarios, including computed tomography and magnetic resonance imaging (MRI), the goal is to reconstruct an image from few of its Fourier domain samples. Many state-of-the-art reconstruction techniques, such as total variation minimization, focus on discrete ‘on-the-grid” modelling of the problem both in spatial domain and Fourier domain. While such discrete-to-discrete models allow for fast algorithms, they can also result in sub-optimal sampling rates and reconstruction artifacts due to model mismatch. Instead, this thesis presents a framework for “off-the-grid”, i.e. continuous domain, recovery of piecewise smooth signals from an optimal number of Fourier samples. The main idea is to model the edge set of the image as the level-set curve of a continuous domain band-limited function. Sampling guarantees can be derived for this framework by investigating the algebraic geometry of these curves. This model is put into a robust and efficient optimization framework by posing signal recovery entirely in Fourier domain as a structured low-rank (SLR) matrix completion problem. An efficient algorithm for this problem is derived, which is an order of magnitude faster than previous approaches for SLR matrix completion. This SLR approach based on off-the-grid modeling shows significant improvement over standard discrete methods in the context of undersampled MRI reconstruction.

In this thesis, chemically reacting flows are studied mainly for detonation problems under 1D, cylindrical and spherical symmetry conditions. The mathematical formulation of chemically reacting, inviscid, unsteady flows with species conservation equations and finite-rate chemistry is described. The Euler equations with finite-rate chemistry are discretized by Finite-Volume method and solved implicitly by using a time-spliting method. Inviscid fluxes are computed using Roe Flux Difference Splitting Model. The numerical solution is implemented in parallel using domain decomposition and PVM library routines for inter-process communication. The solution algorithm is validated first against the numerical and experimental data for a shock tube problem with and without chemical reactions and for a cylindrical and spherical propagation of a shock wave. 1D, cylindrically and spherically symmetric detonations of H2:O2:Ar mixture are studied next.

A mild gasification method has been developed to provide an innovative clean coal technology. The objective of this study is to developed a numerical model to investigate the thermal-flow and gasification process inside a specially designed fluidized-bed mild gasifier using the commercial CFD solver ANSYS/FLUENT. Eulerain-Eulerian method is employed to calculate both the primary phase (air) and secondary phase (coal particles). The Navier-Stokes equations and seven species transport equations are solved with three heterogeneous (gas-solid), two homogeneous (gas-gas) global gasification reactions. Development of the model starts from simulating single-phase turbulent flow and heat transfer to understand the thermal-flow behavior followed by five global gasification reactions, progressively with adding one equation at a time. Finally, the particles are introduced with heterogeneous reactions. The simulation model has been successfully developed. The results are reasonable but require future experimental data for verification.

Novel combustion technologies ensuring low emissions, high efficiency and fuel flexibility are essential to meet the future challenges associated to air pollution, climate change and energy source shortage, as well as to cope with the increasingly stricter environmental regulation. Among them, Moderate or Intense Low oxygen Dilution (MILD) combustion has recently drawn increasing attention. MILD combustion is achieved through the recirculation of flue gases within the reaction region, with the effect of diluting the reactant streams. As a result, the reactivity of the system is reduced, a more uniform reaction zone is obtained, thus leading to decreased NOx and soot emissions. As a consequence of the dilution and enhanced mixing, the ratio between the mixing and chemical time scale is strongly reduced in MILD combustion, indicating the existence of very strong interactions between chemistry and fluid dynamics. In such a context, the use of combustion models that can accurately account for turbulent mixing and detailed chemical kinetics becomes mandatory.Combustion models for conventional flames usually rely on the assumption of time-scale separation (i.e. flamelets and related models), which constrain the thermochemical space accessible in the numerical simulation. Whilst the use of transported PDF methods appears still computationally prohibitive, especially for practical combustion systems, there are a number of closures showing promise for the inclusion of detailed kinetic mechanisms with affordable computational cost. They include the Partially Stirred Reactor (PaSR) approach and the Eddy Dissipation Concept (EDC) model.In order to assess these models under non-conventional MILD combustion conditions, several prototype burners were selected. They include the Adelaide and Delft jet-in-hot coflow (JHC) burners, and the Cabra lifted flames in vitiated coflow. Both Reynolds Averaged Navier Stokes (RANS) and Large Eddy Simulations (LES) were carried out on these burners under various operating conditions and with different fuels. The results indicate the need to explicitly account for both the mixing and chemical time scales in the combustion model formulation. The generalised models developed currently show excellent predictive capabilities when compared with the available, high-fidelity experimental data, especially in their LES formulations. The advanced approaches for the evaluation of the mixing and chemical time scale were compared to several conventional estimation methods, showing their superior performances and wider range of applications. Moreover, the PaSR approach was compared with the steady Flamelet Progress Variable (FPV) model on predicting the lifted Cabra flame, proving that the unsteady behaviours associated to flame extinction and re-ignition should be appropriately considered for such kind of flame.Because of the distributed reaction area, the reacting structures in MILD combustion can be potentially resolved on a Large Eddy Simulation (LES) grid. To investigate that, a comparative study benchmarking the LES predictions for the JHC burner obtained with the PaSR closure and two implicit combustion models was carried out, with the implicit models having filtered source terms coming directly from the Arrhenius expression. Theresults showed that the implicit models are very similar with the conventional PaSR model on predicting the flame properties, for what concerns the mean and root-mean-square of the temperature and species mass fraction fields.To alleviate the cost associated to the use of large kinetic mechanisms, chemistry reduction and tabulation methods to dynamically reduce their size were tested and benchmarked, allowing to allocate the computational resources only where needed. Finally, advanced post-processing tools based on the theory of Computational Singular Perturbation (CSP) were employed to improve the current understanding of flame-turbulence interactions under MILD conditions, confirming the important role of both autoignition and self propagation in these flames. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished