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The primary function of organic light-emitting diodes (OLEDs) is to convert electrons into photons. However, only 25 % of the electronic states (singlets) in electrically excited fluorescent molecules can emit light, which is why triplet harvesting has attracted significant attention. Specifically, one often aims to maximize the rate of triplet-to-singlet conversion, while at the same time, it is crucial to depopulate the singlets fast enough -- before they convert to triplets or interact with other excited states, potentially breaking molecular bonds. Planar microcavities provide a viable architecture to address these issues. By confining the emitters within planar microcavities one can couple the excitons to cavity modes and engineer the population dynamics to one's liking. While the weak-coupling regime is renowned for Purcell-enhanced emission, strongly coupled excitons and photons hybridize to form entirely new energy eigenstates known as polaritons. To fully understand and optimize exciton-photon interactions and light-emission mechanisms across various coupling regimes, a unified theory of optically coupled (and uncoupled) OLEDs is needed. In this article, we introduce a quantum master equation model spanning the zero-, weak-, and strong-coupling regimes. We derive the different rates using Fermi's golden rule and Marcus theory, show how the different regimes converge, and finally evaluate the internal quantum efficiencies in all cases., Comment: 13 pages, 3 figures, 1 table

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray tomography (CBCT) has been limited so far, mainly due to heavy computational loads at clinically relevant 3D resolutions and the difficulty in choosing the regularization parameter. Here an efficient minimization algorithm is presented, combined with a dynamic parameter adjustment based on control theory. The result is a fully automatic 3D reconstruction method running in clinically acceptable time. The input on top of projection data and system geometry is desired degree of sparsity of the reconstruction. This can be determined from an atlas of CT scans, or alternatively used as an easily adjustable parameter with straightforward interpretation., Comment: 15 pages, 4 figures

Planar microcavity polaritons have recently emerged as a promising technology for improving several performance characteristics of organic light-emitting diodes, photodiodes and photovoltaics. To form polaritons and achieve enhanced performance, traditional microcavities with high reflectivity mirrors are fabricated by energy-intensive physical vapor deposition methods, which restrict their use in applications requiring flexibility and low cost. Here, for the first time, we demonstrate a dielectric all-solution-processed polariton microcavity consisting of Rhodamine 6G films in a poly(vinyl alcohol) matrix, exhibiting more than 400 meV Rabi-splitting and photoluminescence with uniform dispersion along the lower polariton mode. Our fully automated deposition and annealing fabrication protocol played a key role in preventing interlayer mixing and producing high optical-quality polariton microcavities, enabling us to observe enhanced scattering of reservoir excitons to the lower polariton and to explore the effects of strong coupling on bimolecular interactions. Notably, we found that polariton microcavities exhibit a more than 10-fold increase in the critical excitation density for bimolecular annihilation compared to bare Rhodamine 6G films. This enhancement can only be partially attributed to the sub-3-fold measured enhancement in radiative lifetime, highlighting the critical role of strong coupling in the influence of molecular dynamics., Comment: 25 pages, 4 figures, supporting information

Parallel-beam X-ray computed tomography (CT) and electrical impedance tomography (EIT) are two imaging modalities which stem from completely different underlying physics, and for decades have been thought to have little in common either practically or mathematically. CT is only mildly ill-posed and uses straight X-rays as measurement energy, which admits simple linear mathematics. However, CT relies on exposing targets to ionizing radiation and requires cumbersome setups with expensive equipment. In contrast, EIT uses harmless electrical currents as measurement energy and can be implemented using simple low-cost portable setups. But EIT is burdened by nonlinearity stemming from the curved paths of electrical currents, as well as extreme ill-posedness which causes characteristic low spatial resolution. In practical EIT reconstruction methods, nonlinearity and ill-posedness have been considered intertwined in a complicated fashion. In this work we demonstrate a surprising connection between CT and EIT which partly unravels the main problems of EIT and leads directly to a proposed imaging modality which we call virtual hybrid parallel-beam tomography (VHPT). We show that hidden deep within EIT data is information which possesses the same linear geometry as parallel-beam CT data. This admits a fundamental restructuring of EIT, separating ill-posedness and nonlinearity into simple modular sub-problems, and yields ''virtual radiographs'' and CT-like images which reveal previously concealed information. Furthermore, as proof of concept we present VHPT images of real-world objects.

The Helsinki Speech Challenge 2024 (HSC2024) invites researchers to enhance and deconvolve speech audio recordings. We recorded a dataset that challenges participants to apply speech enhancement and inverse problems techniques to recorded speech data. This dataset includes paired samples of AI-generated clean speech and corresponding recordings, which feature varying levels of corruption, including frequency attenuation and reverberation. The challenge focuses on developing innovative deconvolution methods to accurately recover the original audio. The effectiveness of these methods will be quantitatively assessed using a speech recognition model, providing a relevant metric for evaluating enhancements in real-world scenarios.

Organic light-emitting diodes (OLEDs) have redefined lighting with their environment-friendliness and flexibility. However, only 25 % of the electronic states of organic molecules can emit light upon electrical excitation, limiting the overall efficiency of OLEDs. Strong light-matter coupling, achieved by confining light within OLEDs using mirrors, creates hybrid light-matter states known as polaritons, which could "activate" the remaining 75 % electronic triplet states. Here, we study triplet-to-polariton transition and derive rates for both reverse inter-system crossing and triplet-triplet annihilation. In addition, we explore how the harmful singlet-singlet annihilation could be reduced with strong coupling., Comment: 10 pages, 4 figures, 1 table, Supplementary Information

A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown target, while some oriented singularities remain invisible in the data. Topological Interface recovery for Limited-angle Tomography, or TILT, is based on lifting the visible part of the wavefront set under a universal covering map. In the space provided, it is possible to connect the appropriate pieces of the lifted wavefront set correctly using dual-tree complex wavelets, a dedicated metric, and persistent homology. The result is not only a suggested invisible boundary but also a computational representation for all interfaces in the target.

Modifying the energy landscape of existing molecular emitters is an attractive challenge with favourable outcomes in chemistry and organic optoelectronic research. It has recently been explored through strong light-matter coupling studies where the organic emitters were placed in an optical cavity. Nonetheless, a debate revolves around whether the observed change in the material properties represents novel coupled system dynamics or the unmasking of pre-existing material properties induced by light-matter interactions. Here, for the first time, we examined the effect of strong coupling in polariton organic light-emitting diodes via time-resolved electroluminescence studies. We accompanied our experimental analysis with theoretical fits using a model of coupled rate equations accounting for all major mechanisms that can result in delayed electroluminescence in organic emitters. We found that in our devices the delayed electroluminescence was dominated by emission from trapped charges and this mechanism remained unmodified in the presence of strong coupling., Comment: 11 pages + 8 supp pages, 4 figures + 8 supp figures

Multi-energy X-ray tomography is studied for decomposing three materials using three X-ray energies and a classical energy-integrating detector. A novel regularization term comprises inner products between the material distribution functions, penalizing any overlap of different materials. The method is tested on real data measured of a phantom embedded with Na$_2$SeO$_3$, Na$_2$SeO$_4$, and elemental selenium. It is found that the two-dimensional distributions of selenium in different oxidation states can be mapped and distinguished from each other with the new algorithm. The results have applications in material science, chemistry, biology and medicine.

Linear optics provides versatile means to simulate and control the dynamics of open quantum systems. Here, the polarization and frequency of photons often represent the system and its environment, respectively. Recently, the photon's path degree of freedom and the effects of interference have been considered as well, giving rise to the concept of "open system interference". Such models have been shown to beat traditional parameter estimation schemes in certain scenarios. In this work, we study the sensitivity of non-Markovian memory effects arising from an open system Mach-Zehnder interferometer. Our protocol provides an alternative way to get around the quantum Cram\'er-Rao theorem, proving itself a noteworthy option for more conventional parameter estimation protocols., Comment: 7 pages, 5 figures

Quantum entanglement and decoherence are the two counterforces of many quantum technologies and protocols. For example, while quantum teleportation is fueled by a pair of maximally entangled resource qubits, it is vulnerable to decoherence. In this Article, we propose an efficient quantum teleportation protocol in the presence of pure decoherence and without entangled resource qubits entering the Bell-state measurement. Instead, we employ multipartite hybrid entanglement between the auxiliary qubits and their local environments within the open-quantum-system context. Interestingly, with a hybrid-entangled initial state, it is the decoherence that allows us to achieve high fidelities. We demonstrate our protocol in an all-optical experiment., Comment: V2: Text changes and title modified. Close to published version

Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along the central direction of projections, leading to poor separation between slices perpendicular to the central direction. A new method is introduced, based on machine learning and geometry, producing an estimate for interfaces between regions of different X-ray attenuation. The estimate can be presented on top of the reconstruction, indicating more reliably the true form and extent of features. The method uses directional edge detection, implemented using complex wavelets and enhanced with morphological operations. By using machine learning, the visible part of the wavefront set is first extracted and then extended to the full domain, filling in the parts of the wavefront set that would otherwise be hidden due to the lack of measurement directions.

Volume conductor problems in cerebral electrophysiology and bioimpedance do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its electrical properties for solving the associated PDEs numerically. Ideally, the model should be made with patient-specific information. In clinical practice, this is not always the case and an average head model is often used. Also, the electrical properties of the tissues might not be completely known due to natural variability. The objective of this work is to develop a 4D (3D+T) statistical anatomical atlas of the electrical properties of the upper part of the human head for cerebral electrophysiology and bioimpedance applications. The atlas is an important tool for in silico studies on cerebral circulation and electrophysiology that require statistically consistent data, e.g., machine learning, sensitivity analyses, and as a benchmark to test inverse problem solvers. The atlas was constructed based on MRI images of human individuals and comprises the electrical properties of the main internal structures and can be adjusted for specific electrical frequencies. The proposed atlas also comprises a time-varying model of arterial brain circulation, based on the solution of the Navier-Stokes equation in the main arteries and their vascular territories. The atlas was successfully used to simulate electrical impedance tomography measurements indicating the necessity of signal-to-noise between 100 and 125dB to identify vascular changes due to the cardiac cycle, corroborating previous studies.

We apply the recently proposed quantum probing protocols with an unknown system-probe coupling to probe the convex coefficients in mixtures of commuting states. By using two reference states instead of one as originally suggested, we are able to probe both lower and upper bounds for the convex coefficient. We perform extensive analysis for the roles of the parameters characterizing the double peaked Gaussian frequency spectrum in the Markovian-to-non-Markovian transition of the polarization dynamics of a single photon. We apply the probing of the convex coefficient to the transition-inducing frequency parameter and show that the non-Markovianity of the polarization dynamics can be confirmed with a single snapshot measurement of the polarization qubit performed at unknown time and even with unknown coupling. We also show how the protocol can identify Markovian and non-Markovian time intervals in the dynamics. The results are validated with single photon experiments.

Dual-energy X-ray tomography is considered in a context where the target under imaging consists of two distinct materials. The materials are assumed to be possibly intertwined in space, but at any given location there is only one material present. Further, two X-ray energies are chosen so that there is a clear difference in the spectral dependence of the attenuation coefficients of the two materials. A novel regularizer is presented for the inverse problem of reconstructing separate tomographic images for the two materials. A combination of two things, (a) non-negativity constraint, and (b) penalty term containing the inner product between the two material images, promotes the presence of at most one material in a given pixel. A preconditioned interior point method is derived for the minimization of the regularization functional. Numerical tests with digital phantoms suggest that the new algorithm outperforms the baseline method, Joint Total Variation regularization, in terms of correctly material-characterized pixels. While the method is tested only in a two-dimensional setting with two materials and two energies, the approach readily generalizes to three dimensions and more materials. The number of materials just needs to match the number of energies used in imaging., Comment: 31 pages, 11 figures, 4 tables

The Hong-Ou-Mandel effect lies at the heart of quantum interferometry, having multiple applications in the field of quantum information processing and no classical counterpart. Despite its popularity, only a few works have considered polarization-frequency interaction within the interferometer. In this paper, we fill this gap. Our system of interest is a general biphoton polarization state that experiences effective dephasing noise by becoming entangled with the same photons' frequency state, as the photons propagate through birefringent media. The photons then meet at a beam splitter, where either coincidence or bunching occurs, after which the polarization-frequency interaction continues on the output paths. Alongside performing extensive theoretical analysis on the coincidence probability and different polarization states, we outline multiple interesting applications that range from constructing Bell states to an alternative delayed choice quantum eraser., Comment: 13 pages, 7 figures

The photographic dataset collected for the Helsinki Deblur Challenge 2021 (HDC2021) contains pairs of images taken by two identical cameras of the same target but with different conditions. One camera is always in focus and produces sharp and low-noise images the other camera produces blurred and noisy images as it is gradually more and more out of focus and has a higher ISO setting. Even though the dataset was designed and captured with the HDC2021 in mind it can be used for any testing and benchmarking of image deblurring algorithms. The data is available here: https://doi.org/10.5281/zenodo.477228

The objective of electrical impedance tomography (EIT) is to reconstruct the internal conductivity of a physical body based on current and voltage measurements at the boundary of the body. In many medical applications the exact shape of the domain boundary and contact impedances are not available. This is problematic as even small errors in the boundary shape of the computation domain or in the contact impedance values can produce large artifacts in the reconstructed images which results in a loss of relevant information. A method is proposed that simultaneously reconstructs the conductivity, the contact impedances and the boundary shape from EIT data. The approach consists of three steps: first, the unknown contact impedances and an anisotropic conductivity reproducing the measured EIT data in a model domain are computed. Second, using isothermal coordinates, a deformation is constructed that makes the conductivity isotropic. The final step minimizes the error of true and reconstructed known geometric properties (like the electrode lengths) using conformal deformations. The feasibility of the method is illustrated with experimental EIT data, with robust and accurate reconstructions of both conductivity and boundary shape., Comment: 34 pages, 17 figures; typos corrected, references added

The dual-tree complex wavelet transform (DT-$\mathbb{C}$WT) is extended to the 4D setting. Key properties of 4D DT-$\mathbb{C}$WT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic three-dimensional target from X-ray projection measurements can be formulated as 4D space-time tomography. The results suggest that 4D DT-$\mathbb{C}$WT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.

We propose alternatives to Bayesian a priori distributions that are frequently used in the study of inverse problems. Our aim is to construct priors that have similar good edge-preserving properties as total variation or Mumford-Shah priors but correspond to well defined infinite-dimensional random variables, and can be approximated by finite-dimensional random variables. We introduce a new wavelet-based model, where the non zero coefficient are chosen in a systematic way so that prior draws have certain fractal behaviour. We show that realisations of this new prior take values in some Besov spaces and have singularities only on a small set $\tau$ that has a certain Hausdorff dimension. We also introduce an efficient algorithm for calculating the MAP estimator, arising from the the new prior, in denoising problem.

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel, we propose to fuse this available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise-ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyze the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed., Comment: 17 pages, 17 figures

Safeguarding the disposal of spent nuclear fuel in a geological repository needs an effective, efficient, reliable and robust non-destructive assay (NDA) system to ensure the integrity of the fuel prior to disposal. In the context of the Finnish geological repository, Passive Gamma Emission Tomography (PGET) will be a part of such an NDA system. We report here on the results of PGET measurements at the Finnish nuclear power plants during the years 2017-2020. Gamma activity profiles are recorded from all angles by rotating the detector arrays around the fuel assembly that has been inserted into the center of the torus. Image reconstruction from the resulting tomographic data is defined as a constrained minimization problem with a data fidelity term and regularization terms. The activity and attenuation maps, as well as detector sensitivity corrections, are the variables in the minimization process. The regularization terms ensure that prior information on the (possible) locations of fuel rods and their diameter are taken into account. Fuel rod classification, the main purpose of the PGET method, is based on the difference of the activity of a fuel rod from its immediate neighbors, taking into account its distance from the assembly center. The classification is carried out by a support vector machine. We report on the results for ten different fuel types with burnups between 5.72 and 55.0 GWd/tU, cooling times between 1.87 and 34.6 years and initial enrichments between 1.9 and 4.4%. For all fuel assemblies measured, missing fuel rods, partial fuel rods and water channels were correctly classified. Burnable absorber fuel rods were classified as fuel rods. On rare occasions, a fuel rod that is present was falsely classified as missing. We conclude that the combination of the PGET device and our image reconstruction method provides a reliable base for fuel rod classification., Comment: 14 pages, 12 figures, 1 table

We combine the dynamics of open quantum systems with interferometry and interference introducing the concept of open system interferometer. By considering a single photon in a Mach-Zehnder interferometer, where the polarization (open system) and frequency (environment) of the photon interact, we theoretically show how inside the interferometer path-wise polarization dephasing dynamics is Markovian while the joint dynamics displays non-Markovian features. Outside the interferometer and due to interference, the open system displays rich dynamical features with distinct alternatives: Only one path displaying non-Markovian memory effects, both paths individually displaying them, or no memory effects appearing at all. Our results also illustrate that measuring the photon's path can either create or destroy non-Markovian memory effects depending on whether the measurement takes place in or outside the interferometer. Moreover, the scheme allows to probe the optical path difference inside the interferometer by studying non-Markovianity outside the interferometer. With our framework and interference, it is also possible to introduce dissipative features for the open system dynamics even though the system-environment interaction itself contains only dephasing. In general, the results open so far unexplored avenues to control open system dynamics and for fundamental studies of quantum physics., Comment: 7 pages, 4 figures

We propose a novel convolutional neural network (CNN), called $\Psi$DONet, designed for learning pseudodifferential operators ($\Psi$DOs) in the context of linear inverse problems. Our starting point is the Iterative Soft Thresholding Algorithm (ISTA), a well-known algorithm to solve sparsity-promoting minimization problems. We show that, under rather general assumptions on the forward operator, the unfolded iterations of ISTA can be interpreted as the successive layers of a CNN, which in turn provides fairly general network architectures that, for a specific choice of the parameters involved, allow to reproduce ISTA, or a perturbation of ISTA for which we can bound the coefficients of the filters. Our case study is the limited-angle X-ray transform and its application to limited-angle computed tomography (LA-CT). In particular, we prove that, in the case of LA-CT, the operations of upscaling, downscaling and convolution, which characterize our $\Psi$DONet and most deep learning schemes, can be exactly determined by combining the convolutional nature of the limited angle X-ray transform and basic properties defining an orthogonal wavelet system. We test two different implementations of $\Psi$DONet on simulated data from limited-angle geometry, generated from the ellipse data set. Both implementations provide equally good and noteworthy preliminary results, showing the potential of the approach we propose and paving the way to applying the same idea to other convolutional operators which are $\Psi$DOs or Fourier integral operators.

In any natural science, measurements are the essential link between theory and observable reality. Is it possible to obtain accurate and relevant information via measurement whose action on the probed system is unknown? In other words, can one be convinced to know something about the nature without knowing in detail how the information was obtained? In this paper, we show that the answer is surprisingly, yes. We construct and experimentally implement a quantum optical probing measurement where measurements on the probes, the photons' polarization states, are used to extract information on the systems, the frequency spectra of the same photons. Unlike the pre-existing probing protocols, our measurement does not require any knowledge of the interaction between the probe and the system., Comment: Accepted for publication. Added theoretical prediction and error bars in figure of measurement results. Added some discussion to outlook

Electrical Impedance Tomography (EIT) is an emerging non-invasive medical imaging modality. It is based on feeding electrical currents into the patient, measuring the resulting voltages at the skin, and recovering the internal conductivity distribution. The mathematical task of EIT image reconstruction is a nonlinear and ill-posed inverse problem. Therefore any EIT image reconstruction method needs to be regularized, typically resulting in blurred images. One promising application is stroke-EIT, or classification of stroke into either ischemic or hemorrhagic. Ischemic stroke involves a blood clot, preventing blood flow to a part of the brain causing a low-conductivity region. Hemorrhagic stroke means bleeding in the brain causing a high-conductivity region. In both cases the symptoms are identical, so a cost-effective and portable classification device is needed. Typical EIT are not optimal for stroke-EIT because of blurriness. This paper explores the possibilities of machine learning in improving the classification results. Two paradigms are compared: (a) learning from the EIT data, that is Dirichlet-to-Neumann (DN) maps and (b) extracting robust features from data and learning from them. The features of choice are Virtual Hybrid Edge Detection (VHED) functions [Greenleaf {\it et al.}, Analysis \& PDE 11, 2018] that have a geometric interpretation and whose computation from EIT data does not involve calculating a full image of the conductivity. We report the measures of accuracy, sensitivity and specificity of the networks trained with EIT data and VHED functions separately. Computational evidence based on simulated noisy EIT data suggests that the regularized grey-box paradigm (b) leads to significantly better classification results than the black-box paradigm (a).

We introduce a method to distribute memory effects among different subspaces of an open two-qubit system's state space. Within the linear optical framework, our system of interest is the polarization of two photons, while the environment consists of their frequency degree of freedom. By exploiting initially correlated frequency distributions and initial frequency-dependent phase factors, we are able to control all the four decoherence functions for polarization -- corresponding to different open system subspace divisions -- almost independently of each other. Hence, our results demonstrate how, in a multipartite dephasing system, Markovian and non-Markovian dynamics can be arbitrarily divided between the subsystems, and giving rise to a novel concept of memory partitions. We also discuss further implications the results have, e.g., on the dynamics of purity and entropy within the two-qubit system., Comment: 9 pages, 4 figures

In this paper we propose a motion-aware variational approach to reconstruct moving objects from sparse dynamic data. The motivation of this work stems from X-ray imaging of plants perfused with a liquid contrast agent, aimed at increasing the contrast of the images and studying the phloem transport in plants over time. The key idea of our approach is to deploy 3D shearlets as a space-temporal prior, treating time as the third dimension. The rationale behind this model is that a continuous evolution of a cartoon-like object is well suited for the use of 3D shearlets. We provide a basic mathematical analysis of the variational model for the image reconstruction. The numerical minimization is carried out with primal-dual scheme coupled with an automated choice of regularization parameter. We test our model on different measurement setups: a simulated phantom especially designed to resemble a plant stem, with spreading points to simulate a spreading contrast agent; a measured agarose gel phantom to demonstrate iodide diffusion and geometry prior to imaging living sample; a measured living tree grown \textit{in vitro} and perfused with a liquid sugar-iodine-mix. The results, compared against a 2D static model, show that our approach provides reconstructions that capture well the time dynamic of the contrast agent onset and are encouraging to develop microCT as a tool to study phloem transport using iodine tracer.

The International Atomic Energy Agency (IAEA) has recently approved passive gamma emission tomography (PGET) as a method for inspecting spent nuclear fuel assemblies (SFAs), an important aspect of international nuclear safeguards which aim at preventing the proliferation of nuclear weapons. The PGET instrument is essentially a single photon emission computed tomography (SPECT) system that allows the reconstruction of axial cross-sections of the emission map of the SFA. The fuel material heavily self-attenuates its gamma-ray emissions, so that correctly accounting for the attenuation is a critical factor in producing accurate images. Due to the nature of the inspections, it is desirable to use as little a priori information as possible about the fuel, including the attenuation map, in the reconstruction process. Current reconstruction methods either do not correct for attenuation, assume a uniform attenuation throughout the fuel assembly, or assume an attenuation map based on an initial filtered back projection (FBP) reconstruction. Here, we propose a method to simultaneously reconstruct the emission and attenuation maps by formulating the reconstruction as a constrained minimization problem with a least squares data fidelity term and regularization terms. Using simulated data, we compare the proposed method to FBP, showing that our approach produces significantly better reconstructions by various numerical metrics and a much better classification of spent, missing, and fresh fuel rods., Comment: 21 pages, 9 figures

Multi-energy CT takes advantage of the non-linearly varying attenuation properties of elemental media with respect to energy, enabling more precise material identification than single-energy CT. The increased precision comes with the cost of a higher radiation dose. A straightforward way to lower the dose is to reduce the number of projections per energy, but this makes tomographic reconstruction more ill-posed. In this paper, we propose how this problem can be overcome with a combination of a regularization method that promotes structural similarity between images at different energies and a suitably selected low-dose data acquisition protocol using non-overlapping projections. The performance of various joint regularization models is assessed with both simulated and experimental data, using the novel low-dose data acquisition protocol. Three of the models are well-established, namely the joint total variation, the linear parallel level sets and the spectral smoothness promoting regularization models. Furthermore, one new joint regularization model is introduced for multi-energy CT: a regularization based on the structure function from the structural similarity index. The findings show that joint regularization outperforms individual channel-by-channel reconstruction. Furthermore, the proposed combination of joint reconstruction and non-overlapping projection geometry enables significant reduction of radiation dose., Comment: 29 pages. Final version: Switched to non-stacked bar graphs for added readability, fixed a typo in the abstract, split previous Figure 5 into 2 Figures (now 5 and 6) for better placement of Figures

The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based methodologies such as deep learning. However, in the context of inverse problems, deep neural networks mostly act as black box routines, used for instance for a somewhat unspecified removal of artifacts in classical image reconstructions. In this paper, we will focus on the severely ill-posed inverse problem of limited angle computed tomography, in which entire boundary sections are not captured in the measurements. We will develop a hybrid reconstruction framework that fuses model-based sparse regularization with data-driven deep learning. Our method is reliable in the sense that we only learn the part that can provably not be handled by model-based methods, while applying the theoretically controllable sparse regularization technique to the remaining parts. Such a decomposition into visible and invisible segments is achieved by means of the shearlet transform that allows to resolve wavefront sets in the phase space. Furthermore, this split enables us to assign the clear task of inferring unknown shearlet coefficients to the neural network and thereby offering an interpretation of its performance in the context of limited angle computed tomography. Our numerical experiments show that our algorithm significantly surpasses both pure model- and more data-based reconstruction methods.

We show that Nachman's integral equations for the Calder\'on problem, derived for conductivities in $W^{2,p}(\Omega)$, still hold for $L^\infty$ conductivities which are $1$ in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of $L^\infty$ conductivities. We rely on Astala-P\"aiv\"arinta's formulation of the Calder\'on problem for a framework in which these convergence results make sense., Comment: 14 pages

This is the documentation of the tomographic X-ray data of cross phantom made available at this https URL The data can be freely used for scientific purposes with appropriate references to the data and to this document in arxiv.org. The data set consists of (1) the X-ray sinogram with 16 or 30 time frames (depending on theresolution) of 2D slices of the phantom and (2) the corresponding static and dynamic measurement matrices modeling the linear operation of the X-ray transform. Each of these sinograms was obtained from a measured 360-projection fan-beam sinogram by down-sampling and taking logarithms. The original (measured) sinogram is also provided in its original form and resolution., Comment: 14 pages, 24 figures. arXiv admin note: substantial text overlap with arXiv:1802.09397, arXiv:1609.07299, arXiv:1705.05732, arXiv:1502.04064

The temporal evolution of entanglement between a noisy system and an ancillary system is analyzed in the context of continuous time open quantum system dynamics. Focusing on a couple of analytically solvable models for qubit systems, we study how Markovian and non-Markovian characteristics influence the problem, discussing in particular their associated entanglement-breaking regimes. These performances are compared with those one could achieve when the environment of the system is forced to return to its input configuration via periodic instantaneous resetting procedures., Comment: Published version, with corrected equations and improved figures

An algorithm is introduced for using electrical surface measurements to detect and monitor cracks inside a two-dimensional conductive body. The technique is based on transforming the probing functions of the classical enclosure method by the Kelvin transform. The transform makes it possible to use virtual discs for probing the interior of the body using electric measurements performed on a flat surface. Theoretical results are presented to enable probing of the full domain to create a profile indicating cracks in the domain. Feasibility of the method is demonstrated with a simulated model of attaching metal sheets together by resistance spot welding.

In this paper, we consider prior-based dimension reduction Kalman filter for undersampled dynamic X-ray tomography. With this method, the X-ray reconstructions are parameterized by a low-dimensional basis. Thus, the proposed method is a) computationally very light; and b) extremely robust as all the computations can be done explicitly. With real and simulated measurement data, we show that the method provides accurate reconstructions even with very limited number of angular directions.

This is the documentation of the tomographic X-ray data of emoji phantom made available at https://zenodo.org/record/1183532#.WpA35Y5rIy1. The data can be freely used for scientific purposes with appropriate references to the data and to this document in arxiv.org. The data set consists of (1) the X-ray sinogram of a single 2D slice of 33 emoji faces (contains 15 different emoji faces) made by small squared ceramic stones and (2) the corresponding static and dynamic measurement matrices modeling the linear operation of the X-ray transform. Each of these sinograms was obtained from a measured 60-projection fan-beam sinogram by down-sampling and taking logarithms. The original (measured) sinogram is also provided in its original form and resolution. The original (measured) sinogram is also provided in its original form and resolution., Comment: arXiv admin note: substantial text overlap with arXiv:1609.07299, arXiv:1705.05732, arXiv:1502.04064

X-ray tomography is a reliable tool for determining the inner structure of 3D object with penetrating X-rays. However, traditional reconstruction methods such as FDK require dense angular sampling in the data acquisition phase leading to long measurement times, especially in X-ray micro-tomography to obtain high resolution scans. Acquiring less data using greater angular steps is an obvious way for speeding up the process and avoiding the need to save huge data sets available memory. However, computing 3D reconstruction from such a sparsely sampled dataset is very sensitive to measurement noise and modelling errors. An automatic regularization method is proposed for robust reconstruction, based on enforcing sparsity in the three-dimensional shearlet transform domain. The inputs of the algorithm are the projection data and {\it a priori} known expected degree of sparsity, denoted $0<{\mathcal C}_{pr}\leq 1$. The number ${\mathcal C}_{pr}$ can be calibrated from a few dense-angle reconstructions and fixed. Human subchondral bone samples were tested and morphometric parameters of the bone reconstructions were then analyzed using standard metrics. The proposed method is shown to outperform the baseline algorithm (FDK) in the case of sparsely collected data. The number of X-ray projections can be reduced up to 10\% of the total amount while retaining the quality of the reconstruction images and of the morphometric paramaters.

In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications, i.e. we do not assume to have a full Radon transform in each time step, but only projections in few angular directions. This restriction enforces a space-time reconstruction, which we perform by incorporating physical motion models and regularization of motion vectors in a variational framework. The methodology of optical flow, which is one of the most common methods to estimate motion between two images, is utilized to formulate a joint variational model for reconstruction and motion estimation. We provide a basic mathematical analysis of the forward model and the variational model for the image reconstruction. Moreover, we discuss the efficient numerical minimization based on alternating minimizations between images and motion vectors. A variety of results are presented for simulated and real measurement data with different sampling strategy. A key observation is that random sampling combined with our model allows reconstructions of similar amount of measurements and quality as a single static reconstruction.

This is the documentation of the tomographic X-ray data of a carved cheese slice. Data are available at www.fips.fi/dataset.php, and can be freely used for scientific purposes with appropriate references to them, and to this document in http://arxiv.org/. The data set consists of (1) the X-ray sinogram of a single 2D slice of the cheese slice with three different resolutions and (2) the corresponding measurement matrices modeling the linear operation of the X-ray transform. Each of these sinograms was obtained from a measured 360-projection fan-beam sinogram by down-sampling and taking logarithms. The original (measured) sinogram is also provided in its original form and resolution., Comment: arXiv admin note: substantial text overlap with arXiv:1609.07299, arXiv:1502.04064