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We consider linear boundary value problems for higher-order parameter-elliptic equations, where the boundary data do not belong to the classical trace spaces. We employ a class of Sobolev spaces of mixed smoothness that admits a generalized boundary trace with values in Besov spaces of negative order. We prove unique solvability for rough boundary data in the half-space and in sufficiently smooth domains. As an application, we show that the operator related to the linearized Cahn--Hilliard equation with dynamic boundary conditions generates a holomorphic semigroup in $L^p(\mathbb R^n_+)\times L^p(\mathbb R^{n-1})$., Comment: 41 pages

Wide-angle video sequences obtained by fisheye cameras exhibit characteristics that may not very well comply with standard image and video processing techniques such as error concealment. This paper introduces a temporal error concealment technique designed for the inherent characteristics of equisolid fisheye video sequences by applying a re-projection into the equisolid domain after conducting part of the error concealment in the perspective domain. Combining this technique with conventional decoder motion vector estimation achieves average gains of 0.71 dB compared against pure decoder motion vector estimation for the test sequences used. Maximum gains amount to up to 2.04 dB for selected frames.

The structured singular value (SSV), or mu, is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or non-repeated complex full blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full blocks. This specific class of uncertainty is relevant for the input output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute a lower bound on SSV for the case of repeated complex full blocks. This generalizes existing power iterations for repeated complex scalar and non-repeated complex full blocks. The upper bound can be formulated as a semi-definite program (SDP), which we solve using a standard interior-point method to compute optimal scaling matrices associated with the repeated full blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full block structure., Comment: Submitted to the International Journal of Robust and Nonlinear Control

Hybrid plasmonic devices involve a nanostructured metal supporting localized surface plasmons to amplify light-matter interaction, and a non-plasmonic material to functionalize charge excitations. Application-relevant epitaxial heterostructures, however, give rise to ballistic ultrafast dynamics that challenge the conventional semiclassical understanding of unidirectional nanometal-to-substrate energy transfer. We study epitaxial Au nanoislands on WSe$_2$ with time- and angle-resolved photoemission spectroscopy and femtosecond electron diffraction: this combination of techniques resolves material, energy and momentum of charge-carriers and phonons excited in the heterostructure. We observe a strong non-linear plasmon-exciton interaction that transfers the energy of sub-bandgap photons very efficiently to the semiconductor, leaving the metal cold until non-radiative exciton recombination heats the nanoparticles on hundreds of femtoseconds timescales. Our results resolve a multi-directional energy exchange on timescales shorter than the electronic thermalization of the nanometal. Electron-phonon coupling and diffusive charge-transfer determine the subsequent energy flow. This complex dynamics opens perspectives for optoelectronic and photocatalytic applications, while providing a constraining experimental testbed for state-of-the-art modelling.

In this paper we introduce a contact process on a dynamical long range percolation (CPDLP) defined on a complete graph $(V,\mathcal{E})$. A dynamical long range percolation is a Feller process defined on the edge set $\mathcal{E}$, which assigns to each edge the state of being open or closed independently. The state of an edge $e$ is updated at rate $v_e$ and is open after the update with probability $p_e$ and closed otherwise. The contact process is then defined on top of this evolving random environment using only open edges for infection while recovery is independent of the background. First, we conclude that an upper invariant law exists and that the phase transitions of survival and non-triviality of the upper invariant coincide. We then formulate a comparison with a contact process with a specific infection kernel which acts as a lower bound. Thus, we obtain an upper bound for the critical infection rate. We also show that if the probability that an edge is open is low for all edges then the CPDLP enters an immunization phase, i.e. it will not survive regardless of the value of the infection rate. Furthermore, we show that on $V=\mathbb{Z}$ and under suitable conditions on the rates of the dynamical long range percolation the CPDLP will almost surely die out if the update speed converges to zero for any given infection rate $\lambda$., Comment: 31 pages, 11 figures, (revised version) Some minor change for clarification and corrections of typos. Article will soon appear in EJP

The rise of variational autoencoders for image and video compression has opened the door to many elaborate coding techniques. One example here is the possibility of conditional interframe coding. Here, instead of transmitting the residual between the original frame and the predicted frame (often obtained by motion compensation), the current frame is transmitted under the condition of knowing the prediction signal. In practice, conditional coding can be straightforwardly implemented using a conditional autoencoder, which has also shown good results in recent works. In this paper, we provide an information theoretical analysis of conditional coding for inter frames and show in which cases gains compared to traditional residual coding can be expected. We also show the effect of information bottlenecks which can occur in practical video coders in the prediction signal path due to the network structure, as a consequence of the data-processing theorem or due to quantization. We demonstrate that conditional coding has theoretical benefits over residual coding but that there are cases in which the benefits are quickly canceled by small information bottlenecks of the prediction signal., Comment: 5 pages, 4 figures, accepted to be presented at PCS 2022. arXiv admin note: text overlap with arXiv:2112.08011 Update Note: Fixed notation in Eq. 10, no changes otherwise

Data-driven techniques for machine vision heavily depend on the training data to sufficiently resemble the data occurring during test and application. However, in practice unknown distortion can lead to a domain gap between training and test data, impeding the performance of a machine vision system. With our proposed approach this domain gap can be closed by unpaired learning of the pristine-to-distortion mapping function of the unknown distortion. This learned mapping function may then be used to emulate the unknown distortion in the training data. Employing a fixed setup, our approach is independent from prior knowledge of the distortion. Within this work, we show that we can effectively learn unknown distortions at arbitrary strengths. When applying our approach to instance segmentation in an autonomous driving scenario, we achieve results comparable to an oracle with knowledge of the distortion. An average gain in mean Average Precision (mAP) of up to 0.19 can be achieved., Comment: 5 pages, 5 figures, accepted for International Conference on Image Processing (ICIP) 2022

The framework of Integral Quadratic Constraints (IQCs) is used to perform an analysis of gradient descent with varying step sizes. Two performance metrics are considered: convergence rate and noise amplification. We assume that the step size is produced from a line search and varies in a known interval. Modeling the algorithm as a linear, parameter-varying (LPV) system, we construct a parameterized linear matrix inequality (LMI) condition that certifies algorithm performance, which is solved using a result for polytopic LPV systems. Our results provide convergence rate guarantees when the step size lies within a restricted interval. Moreover, we recover existing rate bounds when this interval reduces to a single point, i.e. a constant step size. Finally, we note that the convergence rate depends only on the condition number of the problem. In contrast, the noise amplification performance depends on the individual values of the strong convexity and smoothness parameters, and varies inversely with them for a fixed condition number., Comment: 14 pages, 4 figures

An insufficient number of training samples is a common problem in neural network applications. While data augmentation methods require at least a minimum number of samples, we propose a novel, rendering-based pipeline for synthesizing annotated data sets. Our method does not modify existing samples but synthesizes entirely new samples. The proposed rendering-based pipeline is capable of generating and annotating synthetic and partly-real image and video data in a fully automatic procedure. Moreover, the pipeline can aid the acquisition of real data. The proposed pipeline is based on a rendering process. This process generates synthetic data. Partly-real data bring the synthetic sequences closer to reality by incorporating real cameras during the acquisition process. The benefits of the proposed data generation pipeline, especially for machine learning scenarios with limited available training data, are demonstrated by an extensive experimental validation in the context of automatic license plate recognition. The experiments demonstrate a significant reduction of the character error rate and miss rate from 73.74% and 100% to 14.11% and 41.27% respectively, compared to an OCR algorithm trained on a real data set solely. These improvements are achieved by training the algorithm on synthesized data solely. When additionally incorporating real data, the error rates can be decreased further. Thereby, the character error rate and miss rate can be reduced to 11.90% and 39.88% respectively. All data used during the experiments as well as the proposed rendering-based pipeline for the automated data generation is made publicly available under (URL will be revealed upon publication)., Comment: submitted to IEEE Transactions on Intelligent Transportation Systems

In this paper, a novel optical inspection system is presented that is directly suitable for Industry 4.0 and the implementation on IoT-devices controlling the manufacturing process. The proposed system is capable of distinguishing between erroneous and faultless weld seams, without explicitly defining measurement criteria . The developed system uses a deep neural network based classifier for the class prediction. A weld seam dataset was acquired and labelled by an expert committee. Thereby, the visual impression and assessment of the experts is learnt accurately. In the scope of this paper laser triangulation images are used. Due to their special characteristics, the images must be pre-processed to enable the use of a deep neural network. Furthermore, two different approaches are investigated to enable an inspection of differently sized weld seams. Both approaches yield very high classification accuracies of up to 96.88\%, which is competitive to current state of the art optical inspection systems. Moreover, the proposed system enables a higher flexibility and an increased robustness towards systematic errors and environmental conditions due to its ability to generalize. A further benefit of the proposed system is the fast decision process enabling the usage directly within the manufacturing line. Furthermore, standard hardware is used throughout the whole presented work, keeping the roll-out costs for the proposed system as low as possible.

In this paper, we propose a data augmentation framework for Optical Character Recognition (OCR). The proposed framework is able to synthesize new viewing angles and illumination scenarios, effectively enriching any available OCR dataset. Its modular structure allows to be modified to match individual user requirements. The framework enables to comfortably scale the enlargement factor of the available dataset. Furthermore, the proposed method is not restricted to single frame OCR but can also be applied to video OCR. We demonstrate the performance of our framework by augmenting a 15% subset of the common Brno Mobile OCR dataset. Our proposed framework is capable of leveraging the performance of OCR applications especially for small datasets. Applying the proposed method, improvements of up to 2.79 percentage points in terms of Character Error Rate (CER), and up to 7.88 percentage points in terms of Word Error Rate (WER) are achieved on the subset. Especially the recognition of challenging text lines can be improved. The CER may be decreased by up to 14.92 percentage points and the WER by up to 18.19 percentage points for this class. Moreover, we are able to achieve smaller error rates when training on the 15% subset augmented with the proposed method than on the original non-augmented full dataset., Comment: IEEE International Symposium on Signals, Circuits and Systems (ISSCS), 1-4, July 2021

When designing multispectral imaging systems for classifying different spectra it is necessary to choose a small number of filters from a set with several hundred different ones. Tackling this problem by full search leads to a tremendous number of possibilities to check and is NP-hard. In this paper we introduce a novel fast binary search for optimal filter selection that guarantees a minimum distance metric between the different spectra to classify. In our experiments, this procedure reaches the same optimal solution as with full search at much lower complexity. The desired number of filters influences the full search in factorial order while the fast binary search stays constant. Thus, fast binary search allows to find the optimal solution of all combinations in an adequate amount of time and avoids prevailing heuristics. Moreover, our fast binary search algorithm outperforms other filter selection techniques in terms of misclassified spectra in a real-world classification problem.

Using light spectra is an essential element in many applications, for example, in material classification. Often this information is acquired by using a hyperspectral camera. Unfortunately, these cameras have some major disadvantages like not being able to record videos. Therefore, multispectral cameras with wide-band filters are used, which are much cheaper and are often able to capture videos. However, using multispectral cameras requires an additional reconstruction step to yield spectral information. Usually, this reconstruction step has to be done in the presence of imaging noise, which degrades the reconstructed spectra severely. Typically, same or similar pixels are found across the image with the advantage of having independent noise. In contrast to state-of-the-art spectral reconstruction methods which only exploit neighboring pixels by block-based processing, this paper introduces non-local filtering in spectral reconstruction. First, a block-matching procedure finds similar non-local multispectral blocks. Thereafter, the hyperspectral pixels are reconstructed by filtering the matched multispectral pixels collaboratively using a reconstruction Wiener filter. The proposed novel procedure even works under very strong noise. The method is able to lower the spectral angle up to 18% and increase the peak signal-to-noise-ratio up to 1.1dB in noisy scenarios compared to state-of-the-art methods. Moreover, the visual results are much more appealing.

In many image processing tasks it occurs that pixels or blocks of pixels are missing or lost in only some channels. For example during defective transmissions of RGB images, it may happen that one or more blocks in one color channel are lost. Nearly all modern applications in image processing and transmission use at least three color channels, some of the applications employ even more bands, for example in the infrared and ultraviolet area of the light spectrum. Typically, only some pixels and blocks in a subset of color channels are distorted. Thus, other channels can be used to reconstruct the missing pixels, which is called spatio-spectral reconstruction. Current state-of-the-art methods purely rely on the local neighborhood, which works well for homogeneous regions. However, in high-frequency regions like edges or textures, these methods fail to properly model the relationship between color bands. Hence, this paper introduces non-local filtering for building a linear regression model that describes the inter-band relationship and is used to reconstruct the missing pixels. Our novel method is able to increase the PSNR on average by 2 dB and yields visually much more appealing images in high-frequency regions.

Light spectra are a very important source of information for diverse classification problems, e.g., for discrimination of materials. To lower the cost for acquiring this information, multispectral cameras are used. Several techniques exist for estimating light spectra out of multispectral images by exploiting properties about the spectrum. Unfortunately, especially when capturing multispectral videos, the images are heavily affected by noise due to the nature of limited exposure times in videos. Therefore, models that explicitly try to lower the influence of noise on the reconstructed spectrum are highly desirable. Hence, a novel reconstruction algorithm is presented. This novel estimation method is based on the guided filtering technique which preserves basic structures, while using spatial information to reduce the influence of noise. The evaluation based on spectra of natural images reveals that this new technique yields better quantitative and subjective results in noisy scenarios than other state-of-the-art spatial reconstruction methods. Specifically, the proposed algorithm lowers the mean squared error and the spectral angle up to 46% and 35% in noisy scenarios, respectively. Furthermore, it is shown that the proposed reconstruction technique works out-of-the-box and does not need any calibration or training by reconstructing spectra from a real-world multispectral camera with nine channels.

It has been shown, that high resolution images can be acquired using a low resolution sensor with non-regular sampling. Therefore, post-processing is necessary. In terms of video data, not only the spatial neighborhood can be used to assist the reconstruction, but also the temporal neighborhood. A popular and well performing algorithm for this kind of problem is the three-dimensional frequency selective extrapolation (3D-FSE) for which a motion adapted version is introduced in this paper. This proposed extension solves the problem of changing content within the area considered by the 3D-FSE, which is caused by motion within the sequence. Because of this motion, it may happen that regions are emphasized during the reconstruction that are not present in the original signal within the considered area. By that, false content is introduced into the extrapolated sequence, which affects the resulting image quality negatively. The novel extension, presented in the following, incorporates motion data of the sequence in order to adapt the algorithm accordingly, and compensates changing content, resulting in gains of up to 1.75 dB compared to the existing 3D-FSE.

The microscopic origin of slow carrier cooling in lead-halide perovskites remains debated, and has direct implications for applications. Slow carrier cooling has been attributed to either polaron formation or a hot-phonon bottleneck effect at high excited carrier densities (> 10$^{18}$ cm$^{-3}$). These effects cannot be unambiguously disentangled from optical experiments alone. However, they can be distinguished by direct observations of ultrafast lattice dynamics, as these effects are expected to create qualitatively distinct fingerprints. To this end, we employ femtosecond electron diffraction and directly measure the sub-picosecond lattice dynamics of weakly confined CsPbBr$_3$ nanocrystals following above-gap photo-excitation. The data reveal a light-induced structural distortion appearing on a time scale varying between 380 fs to 1200 fs depending on the excitation fluence. We attribute these dynamics to the effect of exciton-polarons on the lattice, and the slower dynamics at high fluences to slower hot carrier cooling, which slows down the establishment of the exciton-polaron population. Further analysis and simulations show that the distortion is consistent with motions of the [PbBr$_3$]$^{-}$ octahedral ionic cage, and closest agreement with the data is obtained for Pb-Br bond lengthening. Our work demonstrates how direct studies of lattice dynamics on the sub-picosecond timescale can discriminate between competing scenarios, thereby shedding light on the origin of slow carrier cooling in lead-halide perovskites.

This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed QCs utilize the sign-indefiniteness of certain classes of quadratic polynomials. These new QCs provide a tight bound on the quadratic terms along specific directions. This reduces the conservatism of the QC bounds as compared to the QCs in previous work. Two numerical examples of local stability analysis are provided to demonstrate the effectiveness of the proposed QCs., Comment: 6 pages, 4 figures, to be published in IEEE Conference on Decision and Control 2022