Shadow of a Colossus: A z=2.45 Galaxy Protocluster Detected in 3D Ly-a Forest Tomographic Mapping of the COSMOS Field

Using moderate-resolution optical spectra from 58 background Lyman-break galaxies and quasars at $z\sim 2.3-3$ within a $11.5'\times13.5'$ area of the COSMOS field ($\sim 1200\,\mathrm{deg}^2$ projected area density or $\sim 2.4\,h^{-1}\,\mathrm{Mpc}$ mean transverse separation), we reconstruct a 3D tomographic map of the foreground Ly$\alpha$ forest absorption at $2.2<z<2.5$ with an effective smoothing scale of $\sigma_{3d}\approx3.5\,h^{-1}\,\mathrm{Mpc}$ comoving. Comparing with 61 coeval galaxies with spectroscopic redshifts in the same volume, we find that the galaxy positions are clearly biased towards regions with enhanced IGM absorption in the tomographic map. We find an extended IGM overdensity with deep absorption troughs at $z=2.45$ associated with a recently-discovered galaxy protocluster at the same redshift. Based on simulations matched to our data, we estimate the enclosed dark matter mass within this IGM overdensity to be $M_{\rm dm} (z=2.45) = (9\pm4)\times 10^{13}\,h^{-1}\,\mathrm{M_\odot}$, and argue based on this mass and absorption strength that it will form at least one $z\sim0$ galaxy cluster with $M(z=0) = (3\pm 2) \times 10^{14}\,h^{-1}\mathrm{M_\odot}$, although its elongated nature suggests that it will likely collapse into two separate clusters. We also point out a compact overdensity of six MOSDEF galaxies at $z=2.30$ within a $r\sim 1\,h^{-1}\,\mathrm{Mpc}$ radius and $\Delta z\sim 0.006$, which does not appear to have a large associated IGM overdensity. These results demonstrate the potential of Ly$\alpha$ forest tomography on larger volumes to study galaxy properties as a function of environment, as well as revealing the large-scale IGM overdensities associated with protoclusters and other features of large-scale structure.Comment: To be submitted to ApJ. Figure 3 can be viewed on Youtube: https://youtu.be/KeW1UJOPMY

Image Quality Improvement in Computed and Binary Tomography

This thesis is the summary of the Author's research in the field of Computed and Binary Tomography. Our main aim was to improve reconstruction quality by developing novel algorithms and improving previous approaches in the research fields of selecting the most informative projection angles, automatic selection of the tube voltage of a CT scanner, and binarizing already reconstructed CT slices using Convolutional Neural Networks

Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation

Sparse representation-based synthetic aperture radar imaging

There is increasing interest in using synthetic aperture radar (SAR) images in automated target recognition and decision-making tasks. The success of such tasks depends on how well the reconstructed SAR images exhibit certain features of the underlying scene. Based on the observation that typical underlying scenes usually exhibit sparsity in terms of such features, we develop an image formation method which formulates the SAR imaging problem as a sparse signal representation problem. Sparse signal representation, which has mostly been exploited in real-valued problems, has many capabilities such as superresolution and feature enhancement for various reconstruction and recognition tasks. However, for problems of complex-valued nature, such as SAR, a key challenge is how to choose the dictionary and the representation scheme for effective sparse representation. Since we are usually interested in features of the magnitude of the SAR reflectivity field, our new approach is designed to sparsely represent the magnitude of the complex-valued scattered field. This turns the image reconstruction problem into a joint optimization problem over the representation of magnitude and phase of the underlying field reflectivities. We develop the mathematical framework for this method and propose an iterative solution for the corresponding joint optimization problem. Our experimental results demonstrate the superiority of this method over previous approaches in terms of both producing high quality SAR images as well as exhibiting robustness to uncertain or limited data

4-D Tomographic Inference: Application to SPECT and MR-driven PET

Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference

Sparse representation-based SAR imaging

There is increasing interest in using synthetic aperture radar (SAR) images in automated target recognition and decision-making tasks. The success of such tasks depends on how well the reconstructed SAR images exhibit certain features of the underlying scene. Based on the observation that typical underlying scenes usually exhibit sparsity in terms of such features, we develop an image formation method which formulates the SAR imaging problem as a sparse signal representation problem. Sparse signal representation, which has mostly been exploited in real-valued problems, has many capabilities such as superresolution and feature enhancement for various reconstruction and recognition tasks. However, for problems of complex-valued nature, such as SAR, a key challenge is how to choose the dictionary and the representation scheme for effective sparse representation. Since we are usually interested in features of the magnitude of the SAR reflectivity field, our new approach is designed to sparsely represent the magnitude of the complex-valued scattered field. This turns the image reconstruction problem into a joint optimization problem over the representation of magnitude and phase of the underlying field reflectivities. We develop the mathematical framework for this method and propose an iterative solution for the corresponding joint optimization problem. Our experimental results demonstrate the superiority of this method over previous approaches in terms of both producing high quality SAR images as well as exhibiting robustness to uncertain or limited data

Tomographic Inverse Problems: Theory and Applications

This was the tenth Oberwolfach conference on the mathematics of tomography. The field rests on the interplay between the theoretical and applied; practical questions lead to new mathematics and pure mathematics motivates new algorithms. This workshop encompassed classical areas such as X-ray computed tomography (CT) as well as new modalities and applications such as dynamic imaging, Compton scattering tomography, hybrid imaging, optical tomography or multi-energy CT and addressed inter alia the use of methods from machine learning