Peter Burgholzer

We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while self-supervised methods allow incomplete ground truth but typically rely on random sampling that, in expectation, covers the entire image. In contrast, we consider fixed, deterministic sampling patterns with inherently incomplete coverage, even in expectation. To overcome this limitation, we exploit multiple invariances of the underlying image distribution, which theoretically allows us to achieve the same reconstruction performance as fully supervised approaches. We validate our method on optical-resolution image upsampling in photoacoustic microscopy (PAM), demonstrating competitive or superior results while requiring substantially less ground truth data.

Infrared thermography nondestructive testing faces challenges due to the diffusive nature of heat, which causes increasing blurring with depth beneath the surface during the reconstruction of internal structures and affects the determination of thermal properties in multilayered materials. This article explores the contextual application of pulse compression and virtual wave methods in active thermography to address these challenges. Pulse compression enables extended, modulated heating of materials and compresses the resulting heat signatures in the time domain. The virtual wave method, on the other hand, transforms temperature signals into virtual propagating damped wave signals, facilitating the reconstruction of defects following the excitation. We analyzed thermal data before and after applying the virtual wave method, and our findings demonstrate enhanced signal-to-noise ratio and high linearity in defect characterization. Building on these insights, we propose a deep spatio-temporal fusion network trained to mimic the virtual wave transformation, thereby enabling efficient and physically guided tomographic reconstruction.

In nondestructive and biomedical imaging, spatial patterns inside a sample are imaged without destroying it. Therefore, propagating waves, including electromagnetic or ultrasonic signals or even diffuse heat, are generated or modified by these internal patterns and transmit this structural information to the sample surface. There, the signals can be detected, and an image of the internal structure can be reconstructed from the measured signals. The amount of information about the interior of the sample that can be obtained from the detected signals at the sample surface is significantly influenced by the propagation from the internal structure to the surface. In the real world, all signal propagation is more or less irreversible. The entropy generated during propagation corresponds to the loss of information. In an idealized model, such propagating waves, called virtual waves, are described by the wave equation. They remain valid solutions of this equation when the direction of time is reversed, thus exhibiting reversibility and showing no entropy production and therefore no loss of information during propagation. A Fredholm integral equation of the first kind relates the diffusion fields locally for each point in space to the virtual waves as their propagating duals. These virtual waves can be calculated from the measured diffusion field at each detection point by inverting this integral equation. In the past, this Fredholm integral was derived using so-called “thermal waves” for thermography. This was often confusing because thermal diffusion cannot be described by the wave equation. Here we derive this relationship for the first time in real space without having to use Fourier frequency space. We have used the locally computed virtual waves from the measured diffusive surface signals for image reconstruction using established time-of-flight methods from ultrasound or radar imaging. This improves the spatial resolution in thermography and compensates for the dispersion of quantum wave packets in atom probe tomography.

In non-destructive and biomedical imaging, spatial patterns inside a sample are imaged without destroying it. Therefore, propagating waves, including electromagnetic or ultrasonic signals, or even diffuse heat are generated or modified by these internal patterns and transmit this structural information to the sample surface. There, the signals can be detected, and an image of the internal structure can be reconstructed from the measured signals. The amount of information about the interior of the sample that can be obtained from the detected signals at the sample surface is significantly influenced by the propagation from the internal structure to the surface. In the real world, all signal propagation is more or less irreversible. The entropy generated during propagation corresponds to the loss of information. In an idealized model, such propagating waves, called virtual waves, are described by the wave equation. They remain valid solutions of this equation when the direction of time is reversed, thus exhibiting reversibility and showing no entropy production and therefore no loss of information during propagation. We have used the locally computed virtual waves from the measured diffusive surface signals for image reconstruction using established time-of-flight methods from ultrasound or RADAR imaging. This improves the spatial resolution in thermography and compensates for the dispersion of quantum wave packets in atom probe tomography.

Bei der zerstörungsfreien Bildgebung breiten sich die Wellen von der abzubildenden Struktur zu einem Detektor aus, wo ihr Signal zur Rekonstruktion des Bildes verwendet wird. Wie bereits Ernst Abbe gezeigt hat, ist die räumliche Auflösung in optischen Mikroskopen durch die Wellenlänge beugungsbegrenzt. In der Akustik, z. B. bei der photoakustischen Bildgebung, wird die detektierbare Wellenlänge nicht nur durch technische Beschränkungen wie die Bandbreite des Akustikdetektors begrenzt, sondern auch durch die frequenzabhängige akustische Dämpfung während der Ausbreitung von der inneren Struktur zum Detektor auf der Probenoberfläche. In der Thermographie bestimmt die Wellenlänge der "Wärmewelle" die räumliche Auflösung. Höhere Frequenzkomponenten mit kleineren Wellenlängen ermöglichen eine bessere räumliche Auflösung. Die höhere Dämpfung von Wärmewellen im Vergleich zur Akustik führt jedoch zu starker Unschärfe und geringer räumlicher Auflösung bei der Abbildung tieferer Strukturen. Mandelis hat einen vereinheitlichenden Rahmen für die Behandlung verschiedener diffusionsbezogener periodischer Phänomene unter dem globalen mathematischen Begriff der Diffusionswellenfelder entwickelt, wie z.B. thermische Wellen aber auch modulierte Wirbelströme. Wellen, die der Wellengleichung genügen, bleiben auch dann gültig Lösung dieser Gleichung, wenn die Zeitrichtung umgekehrt wird, d. h. sie sind zeitinvariant. Diese Eigenschaft ist entscheidend für bildgebende Anwendungen. In der Praxis führen jedoch Phänomene wie Dissipation, Diffusion und Dispersion dazu, dass sich ein Wellenpaket während der Ausbreitung verbreitert. Diese Verbreiterung zerstört die Zeitinvarianz der Welle, was zu einer geringeren räumlichen Auflösung der rekonstruierten Bilder führt. Um dem entgegenzuwirken, wandeln wir diese Wellensignale für jeden Detektorpunkt lokal in „virtuelle Wellen“ um und können dadurch die räumliche Auflösung wesentlich verbessern.

Many non-destructive optical testing methods are currently used for material research, providing various information about material parameters. At RECENDT, a multimodal experimental setup has been designed that combines terahertz (THz) spectroscopy, optical coherence tomography (OCT), infrared (IR), and Raman spectroscopy with a tensile test stage. This setup aims to gather material information such as crystallinity and optical parameters of high-density polyethylene (HDPE) during a tensile test. The setup compares common IR and Raman spectroscopy and the less common optical methods THz and OCT. Complementarity is achieved through different frequency ranges and measurement approaches, resulting in different measured optical material parameters and depths. During tensile testing, HDPE samples with varying crystallinity were analysed, and the determined optical parameters such as refractive index, birefringence, scattering coefficient of decay, and penetration depth can be correlated with the change in crystallinity. These findings demonstrate that the optical methods and their outcomes can be interconnected. With further optimization of the experimental setup, it would be possible to observe the alignment of fibres in fibre composite panels and the stress distribution of polymers effectively. This opens interesting possibilities for polymer characterization in the future, including quality control during moulding processes and material testing.

This study presents photothermal imaging results of subsurface material defects within fiber metal laminates utilizing the virtual wave concept. Therefore, we theoretically analyze the propagation of the virtual wave signal in a hybrid composite laminate via the method of images. For provoking local material damage, the hybrid composite sample is subjected to a defined impact loading. The results obtained from photothermal defect imaging, utilizing rectangular laser pulse excitation, are compared with results obtained from 3D x-ray computed tomography. To sum up, we demonstrate a fast, non-invasive, and easily interpretable reconstruction of defects within macroscopic hybrid composite laminates based on the virtual wave concept.

SignificanceCompressed sensing (CS) uses special measurement designs combined with powerful mathematical algorithms to reduce the amount of data to be collected while maintaining image quality. This is relevant to almost any imaging modality, and in this paper we focus on CS in photoacoustic projection imaging (PAPI) with integrating line detectors (ILDs).AimOur previous research involved rather general CS measurements, where each ILD can contribute to any measurement. In the real world, however, the design of CS measurements is subject to practical constraints. In this research, we aim at a CS-PAPI system where each measurement involves only a subset of ILDs, and which can be implemented in a cost-effective manner.ApproachWe extend the existing PAPI with a self-developed CS unit. The system provides structured CS matrices for which the existing recovery theory cannot be applied directly. A random search strategy is applied to select the CS measurement matrix within this class for which we obtain exact sparse recovery.ResultsWe implement a CS PAPI system for a compression factor of 4:3, where specific measurements are made on separate groups of 16 ILDs. We algorithmically design optimal CS measurements that have proven sparse CS capabilities. Numerical experiments are used to support our results.ConclusionsCS with proven sparse recovery capabilities can be integrated into PAPI, and numerical results support this setup. Future work will focus on applying it to experimental data and utilizing data-driven approaches to enhance the compression factor and generalize the signal class.

In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can nevertheless be overcome and include some concrete technological applications. Describing diffusion as a random walk, one insight is that such a stochastic process involves not only a Gaussian spread of the mean values in space, with the variance proportional to the diffusion time, but also temporal and spatial fluctuations around these mean values. All these fluctuations strongly influence the image reconstruction immediately after the short heating pulse. The Gaussian spread of the mean values in space increases the entropy, while the fluctuations lead to a loss of information that blurs the reconstruction of the initial temperature distribution and can be described mathematically by a spatial convolution with a Gaussian thermal point-spread-function (PSF). The information loss turns out to be equal to the mean entropy increase and limits the spatial resolution proportional to the depth of the imaged subsurface structures. This principal resolution limit can only be overcome by including additional information such as sparsity or positivity. Prior information can be also included by using a deep neural network with a finite degrees of freedom and trained on a specific class of image examples for image reconstruction