Linear Hyperspectral Unmixing Using L0-norm Approximations and Nonnegative Matrix Factorization

Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyperspectral images measured by remote sensors. Most of the existing spectral unmixing algorithms are developed using the linear mixing models. Since the number of endmembers/materials present at each mixed pixel is normally scanty compared with the number of total endmembers (the dimension of spectral library), the problem becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for the linear mixing model through two different scenarios. In the first scenario, the library of spectral signatures is assumed to be known and the main problem is to find the minimum number of endmembers under a reasonable small approximation error. Mathematically, the corresponding problem is called the $\ell_0$-norm problem which is NP-hard problem. Our main study for the first part of thesis is to find more accurate and reliable approximations of $\ell_0$-norm term and propose sparse unmixing methods via such approximations. The resulting methods are shown considerable improvements to reconstruct the fractional abundances of endmembers in comparison with state-of-the-art methods such as having lower reconstruction errors. In the second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing scheme) will be generalized as the blind unmixing scenario that the library of spectral signatures is also estimated. We apply the nonnegative matrix factorization (NMF) method for proposing new unmixing methods due to its noticeable supports such as considering the nonnegativity constraints of two decomposed matrices. Furthermore, we introduce new cost functions through some statistical and physical features of spectral signatures of materials (SSoM) and hyperspectral pixels such as the collaborative property of hyperspectral pixels and the mathematical representation of the concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse unmixing methods for the blind scenario and evaluate the efficiency of the proposed methods via simulations over synthetic and real hyperspectral data sets. The results illustrate considerable enhancements to estimate the spectral library of materials and their fractional abundances such as smaller values of spectral angle distance (SAD) and abundance angle distance (AAD) as well.

Theranostic Fibers for Simultaneous Imaging and Drug Delivery

New methods for creating theranostic systems with simultaneous encapsulation of therapeutic, diagnostic, and targeting agents are much sought after. This work reports for the first time the use of coaxial electrospinning to prepare such systems in the form of core–shell fibers. Eudragit S100 was used to form the shell of the fibers, while the core comprised poly(ethylene oxide) loaded with the magnetic resonance contrast agent Gd(DTPA) (Gd(III) diethylenetriaminepentaacetate hydrate) and indomethacin as a model therapeutic agent. The fibers had linear cylindrical morphologies with clear core–shell structures, as demonstrated by electron microscopy. X-ray diffraction and differential scanning calorimetry proved that both indomethacin and Gd(DTPA) were present in the fibers in the amorphous physical form. This is thought to be a result of intermolecular interactions between the different components, the presence of which was suggested by infrared spectroscopy. In vitro dissolution tests indicated that the fibers could provide targeted release of the active ingredients through a combined mechanism of erosion and diffusion. The proton relaxivities for Gd(DTPA) released from the fibers into tris buffer increased (r1 = 4.79–9.75 s–1 mM–1; r2 = 7.98–14.22 s–1 mM–1) compared with fresh Gd(DTPA) (r1 = 4.13 s–1 mM–1 and r2 = 4.40 s–1 mM–1), which proved that electrospinning has not diminished the contrast properties of the complex. The new systems reported herein thus offer a new platform for delivering therapeutic and imaging agents simultaneously to the colon.

A Simultaneous Equation Approach to Estimating HIV Prevalence with Non-Ignorable Missing Responses

Estimates of HIV prevalence are important for policy in order to establish the health status of a country's population and to evaluate the effectiveness of population-based interventions and campaigns. However, participation rates in testing for surveillance conducted as part of household surveys, on which many of these estimates are based, can be low. HIV positive individuals may be less likely to participate because they fear disclosure, in which case estimates obtained using conventional approaches to deal with missing data, such as imputation-based methods, will be biased. We develop a Heckman-type simultaneous equation approach which accounts for non-ignorable selection, but unlike previous implementations, allows for spatial dependence and does not impose a homogeneous selection process on all respondents. In addition, our framework addresses the issue of separation, where for instance some factors are severely unbalanced and highly predictive of the response, which would ordinarily prevent model convergence. Estimation is carried out within a penalized likelihood framework where smoothing is achieved using a parametrization of the smoothing criterion which makes estimation more stable and efficient. We provide the software for straightforward implementation of the proposed approach, and apply our methodology to estimating national and sub-national HIV prevalence in Swaziland, Zimbabwe and Zambia.

Reduced basis approximations for electromagnetic applications

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016

Hyperspectral unmixing with simultaneous dimensionality estimation

This paper is an elaboration of the simplex identification via split augmented Lagrangian (SISAL) algorithm (Bioucas-Dias, 2009) to blindly unmix hyperspectral data. SISAL is a linear hyperspectral unmixing method of the minimum volume class. This method solve a non-convex problem by a sequence of augmented Lagrangian optimizations, where the positivity constraints, forcing the spectral vectors to belong to the convex hull of the endmember signatures, are replaced by soft constraints. With respect to SISAL, we introduce a dimensionality estimation method based on the minimum description length (MDL) principle. The effectiveness of the proposed algorithm is illustrated with simulated and real data.

Simultaneous volvulus of the transverse and sigmoid colon. Case report

Introduction. Volvulus of transverse colon is rare when compared to cecal and sigmoid volvulus. Cases involving simultaneous volvulus of the transverse colon and another colonic segment are extremely rare. Case report. We report a rare case of simultaneous sigmoid and transverse colon volvulus in a 82-year-old Caucasian female Conclusion. Volvulus is a well recognized cause of large bowel obstruction. The development of transverse and sigmoid volvulus in the same patient is extremely rare. Though rare this possibility must always be considered in the differential diagnosis, when dealing with recurrent intermittent abdominal pain or acute intestinal obstruction.

Simultaneous Meckel’s diverticulitis and appendicitis: a rare complication in puerperium

We report a case of a 24-year-old woman who was delivered via cesarean section at 39 weeks and presented in the puerperium with symptoms of worsening abdominal pain and septicaemia. Preoperative ultrasonography suggested the presence of a pelvic collection. Explorative laparotomy revealed the simultaneous presence of Meckel's diverticulitis and appendicitis without bowel perforation. The patient made an uneventful recovery following small bowel resection with end to end reanastomosis and appendicectomy.

Simultaneous Occurrence of Systemic Lupus Erythematosus, Rheumatoid Arthritis, Hashimoto’s Thyroiditis and Membranous Glomerulonephritis

Introduction: Membranous glomerulonephritis is commonly described in systemic lupus erythematosus (SLE) and hypothyroidism. Clinical presentation: We report a case of a 40-year-old woman who presented with a membranous glomerulonephritis associated with SLE, rheumatoid arthritis and hypothyroidism due to Hashimoto’s thyroiditis. Conclusions: The simultaneous occurrence of these three diseases as possible causes of membranous glomerulonephritis is extremely exceptional.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular we are able to treat "patchy'" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs. Article published and (c) American Physical Society 2007

DopSCAT: A mission concept for simultaneous measurements of marine winds and surface currents

A radar scatterometer operates by transmitting a pulse of microwave energy toward the ocean's surface and measuring the normalized (per-unit-surface) radar backscatter coefficient (σ°). The primary application of scatterometry is the measurement of near-surface ocean winds. By combining σ° measurements from different azimuth angles, the 10 m vector wind can be determined through a Geophysical Model Function (GMF), which relates wind and backscatter. This paper proposes a mission concept for the measurement of both oceanic winds and surface currents, which makes full use of earlier C-band radar remote sensing experience. For the determination of ocean currents, in particular, the novel idea of using two chirps of opposite slope is introduced. The fundamental processing steps required to retrieve surface currents are given together with their associated accuracies. A detailed description of the mission proposal and comparisons between real and retrieved surface currents are presented. The proposed ocean Doppler scatterometer can be used to generate global surface ocean current maps with accuracies better than 0.2 m/s at a spatial resolution better than 25 km (i.e., 12.5 km spatial sampling) on a daily basis. These maps will allow gaining some insights on the upper ocean mesoscale dynamics. The work lies at a frontier, given that the present inability to measure ocean currents from space in a consistent and synoptic manner represents one of the greatest weaknesses in ocean remote sensing.

Simultaneous Acute Pulmonary Embolism and Isolated Septal Myocardial Infarction in a Young Patient

We report here the case of a young patient with a simultaneous isolated septal myocardial infarction (MI) and pulmonary embolism (PE). The aim was to describe a rare clinical entity and to explain why these two pathologies were present at the same time in a young patient.
 A review of literature was established. An interventional cardiologist, an interventional radiologist and a lung specialist were consulted. The diagnostic workup revealed only heterozygous Factor Leiden V mutation. This presentation was probably fortuitous, but worth reporting to our opinion.

A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

Thermotolerant fermenting yeasts for simultaneous saccharification fermentation of lignocellulosic biomass

Lignocellulosic biomass is the most abundant renewable source of energy that has been widely explored as second-generation biofuel feedstock. Despite more than four decades of research, the process of ethanol production from lignocellulosic (LC) biomass remains economically unfeasible. This is due to the high cost of enzymes, end-product inhibition of enzymes, and the need for cost-intensive inputs associated with a separate hydrolysis and fermentation (SHF) process. Thermotolerant yeast strains that can undergo fermentation at temperatures above 40°C are suitable alternatives for developing the simultaneous saccharification and fermentation (SSF) process to overcome the limitations of SHF. This review describes the various approaches to screen and develop thermotolerant yeasts via genetic and metabolic engineering. The advantages and limitations of SSF at high temperatures are also discussed. A critical insight into the effect of high temperatures on yeast morphology and physiology is also included. This can improve our understanding of the development of thermotolerant yeast amenable to the SSF process to make LC ethanol production commercially viable.