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Advancing learned algorithms for 2D X-ray computed tomography
Get PDFThis thesis surveys the intersection of computed tomography (CT) and machine learning (ML), treating CT as an ill-posed inverse problem shaped by object properties, imaging physics, and data limitations. It begins with a foundational overview of CT and the mathematical characterization of tomographic reconstruction, highlighting the need for robust regularization and data-driven strategies. Chapter 2 focuses on tailoring CT acquisitions to the scanned objects, demonstrated by the FleX-ray Lab. It covers scanner functionalities, extension hardware (e.g., sample stages, beam filtration), and acquisition guidelines designed to optimize image quality while managing dose and artifacts. Chapter 3 applies these concepts to multi-material cultural heritage objects, illustrating their impact on image reconstruction and subsequent analysis. Chapter 4 introduces 2DeteCT, a 2D fan-beam CT dataset for developing ML-based reconstruction methods. It details data acquisition, preprocessing, validation, and release, and provides guidance for usage and future extension. Chapter 5 investigates whether training denoising models on simulated noisy data suffices or if experimental noisy data are necessary. Using 2DeteCT and its paired low- and high-dose acquisitions, it scrutinizes the common assumption that simulated noise is adequate for ML training. Chapter 6 presents a benchmarking framework for ML algorithms across CT reconstruction tasks. It offers a reproducible pipeline with standard performance metrics to evaluate full-data, limited- and sparse-angle, low-dose, and beam-hardening–corrected reconstructions, enabling clear comparisons and practical guidance for computational imaging researchers
Quantum versus classical resources in computational complexity
Get PDFThis dissertation studies the interplay between quantum and classical computational resources through the lens of computational complexity theory.
Part I considers low-energy states of quantum systems. We study the complexity of estimating ground- and excited-state energies of local Hamiltonians, given access to a guiding state promised to have non-negligible overlap with the relevant eigenspace. We formalise access models for such guiding states, examine their properties and relations, and study the problem for physically motivated Hamiltonians. We also study the task of obtaining approximate descriptions of ground states, given QMA-oracle access, in the setting of low-locality reduced density matrices.
Part II focuses on quantum probabilistically checkable proof systems (QPCPs). We define a general class of QPCPs that allows adaptivity and multiple unentangled provers, and study its relationship to constant-gap local Hamiltonian problems via quantum reductions. Additionally, we investigate quantum–classical PCPs (QCPCPs), where a quantum verifier has either classical or quantum query access to a classical proof.
Part III explores alternative complexity measures: unitary query complexity and sample complexity. For unitary query complexity, we develop a lower-bound technique based on unitary channel discrimination. In the context of sample complexity, we introduce and analyse a new sample-to-sample task, called complement sampling, and study the power of quantum computation with quantum samples over their classical counterparts
Structural similarity in joint inverse problems
Get PDFJoint inverse problems occur in many practical situations, where different modalities are used to image the same object. Structural similarity is a way to regularize such joint inverse problems by imposing similarity between the images. While structural similarity has found widespread use in many practical settings, its theoretical foundations remain underexplored. This study develops an over-arching formulation for these types of problems and studies their well-posedness via the Direct Method from the calculus of variations. We focus in particular on lower semi-continuity and coerciveness as essential properties for the wellposedness of the variational problem in and . Here quasiconvexity and growth properties of the structural similarity quantifier turns out to be essential. We find that the use of gradient-difference, cross-gradient or Schatten norms as structural similarity quantifiers is theoretically justified. A generalized form of the cross-gradient that inherently works on coupled problems is introduced
Resource requirements for quantum cryptography
Get PDFIn this thesis we explore communication between parties with access to quantum resources, such as channels, qudits, and computers.
We start by studying types of quantum channels. In particular, we consider a scenario where the sender knows a classical description of the qudit they intend to send, and the receiver’s operations are restricted to classical ones. Our main result is that the accuracy of the transmission scales inverse exponentially with the number of pre-shared entangled qudits.
We later look into possible extra properties of quantum channels by giving a protocol for authenticating a noisy channel. Moreover, we prove that our protocol requires access to poly-logarithmic fewer qubits than the previously known techniques.
For the rest of the dissertation we look at what ideal quantum channels could be useful for. Our first result is a round-optimal quantum protocol for oblivious transfer which can be instantiated both in the plain and quantum random oracle models (by basically lifting the properties of an underlying zero-knowledge protocol), but we obtain round optimality in the quantum random oracle model only.
The last chapters of this dissertation are an exploration of a particular set-up assumption, quantum pseudorandomness; i.e. assuming the existence of random (looking) quantum states. We first show that in contrast to the classical case, the size of a quantum pseudorandom object cannot be shrunk. Finally, we prove that if there is a promise problem that admits a quantum reduction that loses information about its input, then certain quantum pseudorandom primitives exit
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Energy-conserving neural network closure model for long-time accurate and stable 2D LES
Get PDFMachine learning-based closure models for LES have shown promise in capturing complex turbulence dynamics but often suffer from instabilities and physical inconsistencies. In this work, we develop a novel skew-symmetric neural architecture as closure model that enforces stability while preserving key physical conservation laws. Our approach leverages a discretization that ensures mass, momentum, and energy conservation, along with a face-averaging filter to maintain mass conservation in coarse-grained velocity fields. We compare our model against several conventional data-driven closures (including unconstrained convolutional neural networks), and the physics-based Smagorinsky model. Performance is evaluated on decaying turbulence and Kolmogorov flow for multiple coarse-graining factors. In these test cases we observe that unconstrained machine learning models suffer from numerical instabilities. In contrast, our skew-symmetric model remains stable across all tests, though at the cost of increased dissipation. Despite this trade-off, we demonstrate that our model still outperforms the Smagorinsky model in unseen scenarios. These findings highlight the potential of structure-preserving machine learning closures for reliable long-time LES
Exact expressions for the unresolved stress in a finite-volume based large-eddy simulation
Get PDFIn this article we propose new discretization-informed expressions for the residual stress tensor (RST) in a finite-volume based large-eddy simulation (LES-FVM). In addition to the classical RST resulting from the non-commutation between filtering and the nonlinear stress, our RST also contains contributions from the numerical flux, discrete divergence, and pressure terms. Unlike the classical RST, our proposed RST is non-symmetric and non-local. The proposed form of the RST is important for generating appropriate reference data for LES closure modeling.
Based on DNS results of the 1D Burgers and 3D incompressible Navier-Stokes equations, we show that the discretization-induced parts of the RST play an important role in the LES-FVM equation for common LES filter widths. When the discrete contribution is included, our RST expression gives zero a-posteriori error in LES, while existing RST expressions give errors that increase over time. For a Smagorinsky model, we show that the Smagorinsky coefficient is higher when fitted to our new RST than when fitted to the classical RST and gives improved results
SQaLe: A large-scale semi-synthetic dataset
No full textSQALE is a large-scale, semi-synthetic Text-to-SQL dataset grounded in real-world database schemas. It was designed to push the boundaries of natural language to SQL generation, combining realistic schema diversity, complex query structures, and linguistically varied natural language questions.
The code for the generation pipeline of this dataset can be accessed on GitHub