Search

We propose an automatic parameter selection strategy for the problem of image super-resolution for images corrupted by blur and additive white Gaussian noise with unknown standard deviation. The proposed approach exploits the structure of both the down-sampling and the blur operators in the frequency domain and computes the optimal regularisation parameter as the one optimising a suitable residual whiteness measure. Computationally, the proposed strategy relies on the fast solution of generalised Tikhonov $\ell_2$-$\ell_2$ problems as proposed in a work from Zhao et al. These problems naturally appear as substeps of the Alternating Direction Method of Multipliers (ADMM) optimisation approach used to solve super-resolution problems with non-quadratic and often non-smooth, sparsity-promoting regularisers both in convex and in non-convex regimes. After detailing the theoretical properties defined in the frequency domain which allow to express the whiteness functional in a compact way, we report an exhaustive list of numerical experiments proving the effectiveness of the proposed approach for different type of problems, in comparison with well-known parameter selection strategy such as, e.g., the discrepancy principle., Comment: arXiv admin note: text overlap with arXiv:2104.01001

To overcome the physical barriers caused by light diffraction, super-resolution techniques are often applied in fluorescence microscopy. State-of-the-art approaches require specific and often demanding acquisition conditions to achieve adequate levels of both spatial and temporal resolution. Analyzing the stochastic fluctuations of the fluorescent molecules provides a solution to the aforementioned limitations, as sufficiently high spatio-temporal resolution for live-cell imaging can be achieved by using common microscopes and conventional fluorescent dyes. Based on this idea, we present COL0RME, a method for COvariance-based $\ell_0$ super-Resolution Microscopy with intensity Estimation, which achieves good spatio-temporal resolution by solving a sparse optimization problem in the covariance domain and discuss automatic parameter selection strategies. The method is composed of two steps: the former where both the emitters' independence and the sparse distribution of the fluorescent molecules are exploited to provide an accurate localization; the latter where real intensity values are estimated given the computed support. The paper is furnished with several numerical results both on synthetic and real fluorescence microscopy images and several comparisons with state-of-the art approaches are provided. Our results show that COL0RME outperforms competing methods exploiting analogously temporal fluctuations; in particular, it achieves better localization, reduces background artifacts and avoids fine parameter tuning., Comment: Accepted manuscript in Biological Imaging and Published online by Cambridge University Press on 16 February 2022. 29 pages and 17 figures

More and more household appliances connect to the Internet and exchange data freely. This is the foundation for true smart buildings. However, there is still no uniform communication technology available, which can connect all appliances from all vendors. Protocols differ between manufacturers making interoperability difficult or even impossible. Manufacturers cannot rely on a reference for the implementation and real estate developers and operators are reluctant to commit to a system until it is clear which one will prevail. A similar situation is evident in smart grids and applies equally to the energy supply industry. This fragmentation ultimately leads to missed opportunities in terms of business models which could connect customers with service providers. We present a first draft of an architecture: SINA - Smart Interoperability Architecture. SINA is based on existing decentralized infrastructure, which avoids creating a dependency of the market participants on an overpowering service provider. The core element of the technical solution is an open-source module integrated in the private clouds of the manufacturers, energy suppliers and service providers. The architecture addresses problems of data ownership, privacy and data security avoiding central administrative structures. It manages data access and transfer in a decentralized and distributed system. SINA uses a blockchain and smart contracts to make sure that the pieces of information about which data are accessed, by whom they are accessed, how they are processed, and which monetary transactions take place are immutably stored and made available. This allows providers to offer services to users in a transparent and trustworthy manner. Finally, SINA includes a matchmaking block which helps service providers find potential customers and vice versa. This set of features makes SINA unique., Comment: 19 pages, 8 figures

In this work we present a dual-mode mid-infrared workflow [6], for detecting sub-superficial mural damages in frescoes artworks. Due to the large nature of frescoes, multiple thermal images are recorded. Thus, the experimental setup may introduce measurements errors, seen as inter-frame changes in the image contrast, after mosaicking. An approach to lowering errors is to post-process the mosaic [10] via osmosis partial differential equation (PDE) [12, 13], which preserves details, mass and balance the lights: efficient numerical study for osmosis on large images is proposed [2, 11], based on operator splitting [8]. Our range of Cultural Heritage applications include the detection of sub-superficial voids in Monocromo (L. Da Vinci, Castello Sforzesco, Milan) [5], the light-balance for multi-spectral imaging and the data integration on the Archimedes Palimpsest [10]., Comment: 3 pages, 6 figures

We present results of the Relic Axion Dark-Matter Exploratory Setup (RADES), a detector which is part of the CERN Axion Solar Telescope (CAST), searching for axion dark matter in the 34.67$\mu$eV mass range. A radio frequency cavity consisting of 5 sub-cavities coupled by inductive irises took physics data inside the CAST dipole magnet for the first time using this filter-like haloscope geometry. An exclusion limit with a 95% credibility level on the axion-photon coupling constant of g$_{a\gamma}\gtrsim 4\times10^{-13} \text{GeV}^{-1}$ over a mass range of 34.6738 $\mu$eV < $m_a$ < 34.6771 $\mu$eV is set. This constitutes a significant improvement over the current strongest limit set by CAST at this mass and is at the same time one of the most sensitive direct searches for an axion dark matter candidate above the mass of 25 $\mu$eV. The results also demonstrate the feasibility of exploring a wider mass range around the value probed by CAST-RADES in this work using similar coherent resonant cavities., Comment: 14 pages, 9 figures. Accepted for publication in JHEP. Minor changes done compared to the previous version

Over the last 30 years a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned in basic courses in mathematical image processing is the celebrated Rudin-Osher-Fatemi (ROF) model \cite{ROF} which relies on the minimisation of the edge-preserving Total Variation (TV) semi-norm as regularisation term. Despite its (often limiting) simplicity, this model is still very much employed in many applications and used as a benchmark for assessing the performance of modern learning-based image reconstruction approaches, thanks to its thorough analytical and numerical understanding. Among the many extensions to TV proposed over the years, a large class is based on the concept of \emph{space variance}. Space-variant models can indeed overcome the intrinsic inability of TV to describe \emph{local} features (strength, sharpness, directionality) by means of an adaptive mathematical modelling which accommodates local regularisation weighting, variable smoothness and anisotropy. Those ideas can further be cast in the flexible Bayesian framework of generalised Gaussian distributions and combined with maximum likelihood and hierarchical optimisation approaches for efficient hyper-parameter estimation. In this work, we review and connect the major contributions in the field of space-variant TV-type image reconstruction models, focusing, in particular, on their Bayesian interpretation which paves the way to new exciting and unexplored research directions.

We propose an automatic parameter selection strategy for variational image super-resolution of blurred and down-sampled images corrupted by additive white Gaussian noise (AWGN) with unknown standard deviation. By exploiting particular properties of the operators describing the problem in the frequency domain, our strategy selects the optimal parameter as the one optimising a suitable residual whiteness measure. Numerical tests show the effectiveness of the proposed strategy for generalised $\ell_2$-$\ell_2$ Tikhonov problems.

In this note, we consider a special instance of the scaled, inexact and adaptive generalised Fast Iterative Soft-Thresholding Algorithm (SAGE-FISTA) recently proposed in (Rebegoldi, Calatroni, '21) for the efficient solution of strongly convex composite optimisation problems. In particular, we address here the sole (non-strongly) convex optimisation scenario, which is frequently encountered in many imaging applications. The proposed inexact S-FISTA algorithm shows analogies to the variable metric and inexact version of FISTA studied in (Bonettini, Rebegoldi, Ruggiero, '19), the main difference being the use of an adaptive (non-monotone) backtracking strategy allowing for the automatic adjustment of the algorithmic step-size along the iterations (see (Scheinberg, Goldfarb, Bai, '14, Calatroni, Chambolle, '19)). A quadratic convergence result in function values depending on the backtracking parameters and the upper and lower bounds on the spectrum of the variable metric operators is given. Experimental results on TV image deblurring problems with Poisson noise are then reported for numerical validation, showing improved computational efficiency and precision.

We consider a variable metric and inexact version of the FISTA-type algorithm considered in (Chambolle, Pock, 2016, Calatroni, Chambolle, 2019) for the minimization of the sum of two (possibly strongly) convex functions. The proposed algorithm is combined with an adaptive (non-monotone) backtracking strategy, which allows for the adjustment of the algorithmic step-size along the iterations in order to improve the convergence speed. We prove a linear convergence result for the function values, which depends on both the strong convexity moduli of the two functions and the upper and lower bounds on the spectrum of the variable metric operators. We validate the proposed algorithm, named Scaled Adaptive GEneralized FISTA (SAGE-FISTA), on exemplar image denoising and deblurring problems where edge-preserving Total Variation (TV) regularization is combined with Kullback-Leibler-type fidelity terms, as it is common in applications where signal-dependent Poisson noise is assumed in the data.

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional architecture of V1 based on both local and lateral connections. For the numerical realisation of both models, we consider standard gradient descent algorithms combined with Fourier-based approaches for the efficient computation of the sub-Laplacian evolution. Our numerical results show that the use of the sub-Riemannian kernel allows to reproduce numerically visual misperceptions and inpainting-type biases in a stronger way in comparison with the previous approaches.

Super-resolution light microscopy overcomes the physical barriers due to light diffraction, allowing for the observation of otherwise indistinguishable subcellular entities. However, the specific acquisition conditions required by state-of-the-art super-resolution methods to achieve adequate spatio-temporal resolution are often very challenging. Exploiting molecules fluctuations allows good spatio-temporal resolution live-cell imaging by means of common microscopes and conventional fluorescent dyes. In this work, we present the method COL0RME for COvariance-based $\ell_0$ super-Resolution Microscopy with intensity Estimation. It codifies the assumption of sparse distribution of the fluorescent molecules as well as the temporal and spatial independence between emitters via a non-convex optimization problem formulated in the covariance domain. In order to deal with real data, the proposed approach also estimates background and noise statistics. It also includes a final estimation step where intensity information is retrieved, which is valuable for biological interpretation and future applications to super-resolution imaging.

We propose a continuous non-convex variational model for Single Molecule Localisation Microscopy (SMLM) super-resolution in order to overcome light diffraction barriers. Namely, we consider a variation of the Continuous Exact $\ell_0$ (CEL0) penalty recently introduced to relax the $\ell_2-\ell_0$ problem where a weighted-$\ell_2$ data fidelity is considered to model signal-dependent Poisson noise. For the numerical solution of the associated minimisation problem, we consider an iterative reweighted $\ell_1$ (IRL1) strategy for which we detail efficient parameter computation strategies. We report qualitative and quantitative molecule localisation results showing that the proposed weighted-CEL0 (wCEL0) model improves the results obtained by CEL0 and state-of-the art deep-learning approaches for the high-density SMLM ISBI 2013 dataset.

We propose a non-convex variational model for the super-resolution of Optical Coherence Tomography (OCT) images of the murine eye, by enforcing sparsity with respect to suitable dictionaries learnt from high-resolution OCT data. The statistical characteristics of OCT images motivate the use of {\alpha}-stable distributions for learning dictionaries, by considering the non-Gaussian case, {\alpha}=1. The sparsity-promoting cost function relies on a non-convex penalty - Cauchy-based or Minimax Concave Penalty (MCP) - which makes the problem particularly challenging. We propose an efficient algorithm for minimizing the function based on the forward-backward splitting strategy which guarantees at each iteration the existence and uniqueness of the proximal point. Comparisons with standard convex L1-based reconstructions show the better performance of non-convex models, especially in view of further OCT image analysis, Comment: 4 pages, 2 figures, 1 table, 1 algorithm, submitted to ISBI2021

We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic $\ell^0$ regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in [1] for general signal recovery problems. For the numerical realisation of the model, we propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugate-gradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that $\ell^0$ gradient-regularised super-resolved images can be effectively used to improve the accuracy of standard segmentation algorithms when applied to QR and cell detection, and landcover classification problems, in comparison to the results achieved by other approaches., Comment: 10 pages + appendices, 7 figures

Vacuum electrical breakdowns, also known as vacuum arcs, are a limiting factor in many devices that are based on application of high electric fields near their component surfaces. Understanding of processes that lead to breakdown events may help mitigating their appearance and suggest ways for improving operational efficiency of power-consuming devices. Stability of surface performance at a given value of the electric field is affected by the conditioning state, i.e. how long the surface was exposed to this field. Hence, optimization of the surface conditioning procedure can significantly speed up the preparatory steps for high-voltage applications. In this article, we use pulsed dc systems to optimize the surface conditioning procedure of copper electrodes, focusing on the effects of voltage recovery after breakdowns, variable repetition rates as well as long waiting times between pulsing runs. Despite the differences in the experimental scales, ranging from $10^{-4}$ s between pulses, up to pulsing breaks of $10^5$ s, the experiments show that the longer the idle time between the pulses, the more probable it is that the next pulse produces a breakdown. We also notice that secondary breakdowns, i.e. those which correlate with the previous ones, take place mainly during the voltage recovery stage. We link these events with deposition of residual atoms from vacuum on the electrode surfaces. Minimizing the number of pauses during the voltage recovery stage reduces power losses due to secondary breakdown events improving efficiency of the surface conditioning., Comment: 14 pages, 11 figures. Submitted to Physical Review Accelerators and Beams

This lecture gives an introduction to the basic physics of the electrical conductivity of metals, its temperature dependence and its limiting factors. We will then introduce the concept of surface resistance, of high relevance in accelerators for its link with beam impedance and for RF applications, including notions related to the anomalous skin effect. The surface resistance will help establishing a link to heat exchanges between bodies by radiation, and to the concept of emissivity. Thermal conductivity will then be introduced, discussing both its electron and phonon exchange components, and the relevant limiting factors., Comment: 20 pages, contribution to the CAS - CERN Accelerator School: Vacuum for Particle Accelerators, 6-16 June 2017, Glumsl\"ov, Sweden

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we analyze both convergence and stability. Using tools from inexact proximal calculus, we prove early stopping results with optimal convergence rates for additive data-fit terms as well as more general cases, such as the Kullback-Leibler divergence, for which different type of proximal point approximations hold.

Understanding the microscopic phenomena behind vacuum arc ignition and generation is crucial for being able to control the breakdown rate, thus improving the effectiveness of many high-voltage applications where frequent breakdowns limit the operation. In this work, statistical properties of various aspects of breakdown, such as the number of pulses between breakdowns, breakdown locations and crater sizes are studied independently with almost identical Pulsed DC Systems at the University of Helsinki and in CERN. In high-gradient experiments, copper electrodes with parallel plate capacitor geometry, undergo thousands of breakdowns. The results support the classification of the events into primary and secondary breakdowns, based on the distance and number of pulses between two breakdowns. Primary events follow a power law on the log--log scale with the slope $\alpha \approx 1.33$, while the secondaries are highly dependent on the pulsing parameters., Comment: 11 pages, 13 figures

We consider the evolution model proposed in [9, 6] to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with the widely used Wilson-Cowan equations [48], mainly in terms of efficient representation properties. Then, in order to explicitly encode local directional information, we exploit the model of the primary visual cortex (V1) proposed in [20] and largely used over the last years for several image processing problems [24,38,28]. The resulting model is thus defined in the space of positions and orientation and it is capable to describe assimilation and contrast visual bias at the same time. We report several numerical tests showing the ability of the model to reproduce, in particular, orientation-dependent phenomena such as grating induction and a modified version of the Poggendorff illusion. For this latter example, we empirically show the existence of a set of threshold parameters differentiating from inpainting to perception-type reconstructions and describing long-range connectivity between different hypercolumns in V1., Comment: This is the revised extended invited journal version of the SSVM 2019 conference proceeding arXiv:1812.07425

We propose a new variational model for non-linear image fusion. Our approach is based on the use of an osmosis energy term related to the one studied in Vogel et al. (2013) and Weickert et al. (2013) The minimization of the proposed non-convex energy realizes visually plausible image data fusion, invariant to multiplicative brightness changes. On the practical side, it requires minimal supervision and parameter tuning and can encode prior information on the structure of the images to be fused. For the numerical solution of the proposed model, we develop a primal-dual algorithm and we apply the resulting minimization scheme to solve multi-modal face fusion, color transfer and cultural heritage conservation problems. Visual and quantitative comparisons to state-of-the-art approaches prove the out-performance and the flexibility of our method., Comment: 10 pages, 8 figures

In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes from the statistical assumption that the gradients of the target image distribute locally according to space-variant bivariate Laplacian distributions. The highly flexible variational structure of the corresponding regularizer encodes several free parameters which hold the potential for faithfully modelling the local geometry in the image and describing local orientation preferences. For an automatic estimation of such parameters, we design a robust maximum likelihood approach and report results on its reliability on synthetic data and natural images. A minimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) is presented for the efficient numerical solution of the proposed variational model. Some experimental results are reported which demonstrate the high-quality of restorations achievable by the proposed model, in particular with respect to classical Total Variation regularization.

In this work we have aimed to reproduce supra-threshold perception phenomena, specifically visual illusions, with Wilson-Cowan-type models of neuronal dynamics. We have found that it is indeed possible to do so, but that the ability to replicate visual illusions is related to how well the neural activity equations comply with the efficient representation principle. Our first contribution is to show that the Wilson-Cowan equations can reproduce a number of brightness and orientation-dependent illusions, and that the latter type of illusions require that the neuronal dynamics equations consider explicitly the orientation, as expected. Then, we formally prove that there can't be an energy functional that the Wilson-Cowan equations are minimizing, but that a slight modification makes them variational and yields a model that is consistent with the efficient representation principle. Finally, we show that this new model provides a better reproduction of visual illusions than the original Wilson-Cowan formulation.

We propose an efficient estimation technique for the automatic selection of locally-adaptive Total Variation regularisation parameters based on an hybrid strategy which combines a local maximum-likelihood approach estimating space-variant image scales with a global discrepancy principle related to noise statistics. We verify the effectiveness of the proposed approach solving some exemplar image reconstruction problems and show its outperformance in comparison to state-of-the-art parameter estimation strategies, the former weighting locally the fit with the data (Dong et al. '11), the latter relying on a bilevel learning paradigm (Hinterm\"uller et al., '17)

Conditioning of a metal structure in a high-voltage system is the progressive development of resistance to vacuum arcing over the operational life of the system. This is, for instance, seen during the initial operation of radio frequency (rf) cavities in particle accelerators. It is a relevant topic for any technology where breakdown limits performance, and where conditioning continues for a significant duration of system runtime. Projected future linear accelerators require structures with accelerating gradients of up to 100 MV/m. Currently, this performance level is only achievable after a multi-month conditioning period. In this work, a pulsed DC system applying voltage pulses over parallel disk electrodes was used to study the conditioning process, with the objective of obtaining insight into its underlying mechanics, and ultimately, to find ways to shorten the conditioning process. Two kinds of copper electrodes were tested: As-prepared machine-turned electrodes ("hard" copper), and electrodes that additionally had been subjected to high temperature treatments ("soft" copper). The conditioning behaviour of the soft electrodes was found to be similar to that of comparably treated accelerating structures, indicating a similar conditioning process. The hard electrodes reached the same ultimate performance as the soft electrodes much faster, with a difference of more than an order of magnitude in the number of applied voltage pulses. Two distinctly different distributions of breakdown locations were observed on the two types of electrodes. Considered together, our results support the crystal structure dislocation theory of breakdown, and suggest that the conditioning of copper in high field systems such as rf accelerating structures is dominated by material hardening.