arXiv subjects

Peter Burgholzer

Publications and source records attributed to Peter Burgholzer.

17 recordsLinked to original sources

arXiv2025

Locally-Supervised Global Image Restoration

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.

cs.CV↗

arXiv2025

Linking diffusive fields to virtual waves as their propagative duals

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.

physics.app-ph↗

arXiv2024

Design, Implementation and Analysis of a Compressed Sensing Photoacoustic Projection Imaging System

Significance: Compressed 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). Aim: Our 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. Approach: We 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. Results: We 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. Conclusions: CS 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.

cs.CV↗

arXiv2023

Breaking the Resolution limit in Photoacoustic Imaging using Positivity and Sparsity

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

math.NA↗

arXiv2023

Heat diffusion blurs photothermal images with increasing depth

math.NA↗

arXiv2023

Sampling and resolution in sparse view photoacoustic tomography

We investigate resolution in photoacoustic tomography (PAT). Using Shannon theory, we investigate the theoretical resolution limit of sparse view PAT theoretically, and empirically demonstrate that all reconstruction methods used exceed this limit.

math.NA↗

arXiv2020

Linking information theory and thermodynamics to spatial resolution in photothermal and photoacoustic imaging

In this tutorial, we combine the different scientific fields of information theory, thermodynamics, regularization theory and non-destructive imaging, especially for photoacoustic and photothermal imaging. The goal is to get a better understanding of how information gaining for subsurface imaging works and how the spatial resolution limit can be overcome by using additional information. Here, the resolution limit in photoacoustic and photothermal imaging is derived from the irreversibility of attenuation of the pressure wave and of heat diffusion during propagation of the signals from the imaged subsurface structures to the sample surface, respectively. The acoustic or temperature signals are converted into so-called virtual waves, which are their reversible counterparts and which can be used for image reconstruction by well-known ultrasound reconstruction methods. The conversion into virtual waves is an ill-posed inverse problem which needs regularization. The reason for that is the information loss during signal propagation to the sample surface, which turns out to be equal to the entropy production. As the entropy production from acoustic attenuation is usually small compared to the entropy production from heat diffusion, the spatial resolution in acoustic imaging is higher than in thermal imaging. Therefore, it is especially necessary to overcome this resolution limit for thermographic imaging by using additional information. Incorporating sparsity and non-negativity in iterative regularization methods gives a significant resolution enhancement, which was experimentally demonstrated by one-dimensional imaging of thin layers with varying depth or by three-dimensional imaging, either from a single detection plane or from three perpendicular detection planes on the surface of a sample cube.

physics.app-ph↗

arXiv2020

Laser excited super resolution thermal imaging for nondestructive inspection of internal defects

A photothermal super resolution technique is proposed for an improved inspection of internal defects. To evaluate the potential of the laser-based thermographic technique, an additively manufactured stainless steel specimen with closely spaced internal cavities is used. Four different experimental configurations in transmission, reflection, stepwise and continuous scanning are investigated. The applied image post-processing method is based on compressed sensing and makes use of the block sparsity from multiple measurement events. This concerted approach of experimental measurement strategy and numerical optimization enables the resolution of internal defects and outperforms conventional thermographic inspection techniques.

physics.app-ph↗

arXiv2019

NETT Regularization for Compressed Sensing Photoacoustic Tomography

We discuss several methods for image reconstruction in compressed sensing photoacoustic tomography (CS-PAT). In particular, we apply the deep learning method of [H. Li, J. Schwab, S. Antholzer, and M. Haltmeier. NETT: Solving Inverse Problems with Deep Neural Networks (2018), arXiv:1803.00092], which is based on a learned regularizer, for the first time to the CS-PAT problem. We propose a network architecture and training strategy for the NETT that we expect to be useful for other inverse problems as well. All algorithms are compared and evaluated on simulated data, and validated using experimental data for two different types of phantoms. The results on the one the hand indicate great potential of deep learning methods, and on the other hand show that significant future work is required to improve their performance on real-word data.

math.NA↗

arXiv2018

A Linear State Space Model for Photoacoustic Imaging in an Acoustic Attenuating Media

In photoacoustic imaging, ultrasound waves generated by a temperature rise after illumination of light absorbing structures are measured on the sample surface. These measurements are then used to reconstruct the optical absorption. We develop a method for reconstructing the absorption inside the sample based on a discrete linear state space reformulation of a partial differential equation that describes the propagation of the ultrasound waves. Fundamental properties of the corresponding state space model such as stability, observability and controllability are also analyzed. By using Stokes' equation, the frequency dependent attenuation of the ultrasound waves is incorporated into our model, therefore the proposed method is of general nature. As a consequence, this approach allows for inhomogeneous probes with arbitrary absorption profiles and it accounts for the decrease in laser intensity due to absorption. Furthermore, it provides a method for optimizing the laser modulation signal such that the accuracy of the estimated absorption profile is maximized. Utilizing the optimized laser modulation signal yields an increase in reconstruction accuracy compared to short laser pulses as well as chirp modulation in many scenarios.

physics.app-ph↗

arXiv2017

A New Sparsification and Reconstruction Strategy for Compressed Sensing Photoacoustic Tomography

Compressed sensing (CS) is a promising approach to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. This allows to increase the measurement speed and to reduce system costs. Instead of collecting point-wise measurements, in CS one uses various combinations of pressure values at different sensor locations. Sparsity is the main condition allowing to recover the photoacoustic (PA) source from compressive measurements. In this paper we introduce a new concept enabling sparse recovery in CS PAT. Our approach is based on the fact that the second time derivative applied to the measured pressure data corresponds to the application of the Laplacian to the original PA source. As typical PA sources consist of smooth parts and singularities along interfaces the Laplacian of the source is sparse (or at least compressible). To efficiently exploit the induced sparsity we develop a reconstruction framework to jointly recover the initial and the modified sparse source. Reconstruction results with simulated as well as experimental data are given.

math.NA↗

arXiv2017

Information loss and entropy production during dissipative processes in a macroscopic system kicked out of the equilibrium

In macroscopic systems behavior is usually reproducible and fluctuations, which are deviations from the typically observed mean values, are small. But almost all inverse problems in the physical and biological sciences are ill-posed and these fluctuations are highly 'amplified'. Using stochastic thermodynamics we describe a system in equilibrium kicked to a state far from equilibrium and the following dissipative process back to equilibrium. From the observed value at a certain time after the kick the magnitude of the kick should be estimated, which is such an ill-posed inverse problem and fluctuations get relevant. For the model system of a kicked Brownian particle the time-dependent probability distribution, the information loss about the magnitude of the kick described by the Kullback-Leibler divergence, and the entropy production derived from the observed mean values are given. The equality of information loss caused by fluctuations and mean entropy production is shown for general kicked dissipative processes from stochastic thermodynamics following the derivation of the Jarzynski and Crooks equalities. The information-theoretical interpretation of the Kullback-Leibler divergence (Chernoff-Stein Lemma) allows us to describe the influence of the fluctuations without knowing their distributions just from the mean value equations and thus to derive very applicable results, e.g., by giving thermodynamic limits of spatial resolution for imaging.

cond-mat.stat-mech↗

arXiv2017

Three-dimensional thermographic imaging using a virtual wave concept

In this work, it is shown that image reconstruction methods from ultrasonic imaging can be employed for thermographic signals. Before using these imaging methods, a virtual signal is calculated by applying a local transformation to the temperature evolution measured on a sample surface. The introduced transformation describes all the irreversibility of the heat diffusion process and can be used for every sample shape. To date, one-dimensional methods have been primarily used in thermographic imaging. The proposed two-stage algorithm enables reconstruction in two and three dimensions. The feasibility of this approach is demonstrated through simulations and experiments. For the latter, small steel beads embedded in an epoxy resin are imaged. The resolution limit is found to be proportional to the depth of the structures and to be inversely proportional to the logarithm of the signal-to-noise ratio. Limited-view artefacts can arise if the measurement is performed on a single planar detection surface. These artifacts can be reduced by measuring the thermographic signals from multiple planes, which is demonstrated by numerical simulations and by experiments performed on an epoxy cube.

physics.data-an↗

arXiv2016

Compressed sensing and sparsity in photoacoustic tomography

Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this issue using techniques of compressed sensing. We demonstrate, that the number of measurements can significantly be reduced by allowing general linear measurements instead of point-wise pressure values. A main requirement in compressed sensing is the sparsity of the unknowns to be recovered. For that purpose we develop the concept of sparsifying temporal transforms for three-dimensional photoacoustic tomography. We establish a two-stage algorithm that recovers the complete pressure Signals in a first step and then applies a standard reconstruction algorithm such as back-projection. This yields a novel reconstruction method with much lower complexity than existing compressed sensing approaches for photoacoustic tomography. Reconstruction results for simulated and for experimental data verify that the proposed compressed sensing scheme allows to significantly reducing the number of spatial measurements without reducing the spatial resolution.

math.NA↗

arXiv2015

Thermodynamic Limits of Spatial Resolution in Active Thermography

Thermal waves are caused by pure diffusion: their amplitude is decreased by more than a factor of 500 within a propagation distance of one wavelength. The diffusion equation, which describes the temperature as a function of space and time, is linear. For every linear equation the superposition principle is valid, which is known as Huygens principle for optical or mechanical wave fields. This limits the spatial resolution, like the Abbe diffraction limit in optics. The resolution is the minimal size of a structure which can be detected at a certain depth. If an embedded structure at a certain depth in a sample is suddenly heated, e.g. by eddy current or absorbed light, an image of the structure can be reconstructed from the measured temperature at the sample surface. To get the resolution the image reconstruction can be considered as the time reversal of the thermal wave. This inverse problem is ill-conditioned and therefore regularization methods have to be used taking additional assumptions like smoothness of the solutions into account. In the present work for the first time methods of non-equilibrium statistical physics are used to solve this inverse problem without the need of such additional assumptions and without the necessity to choose a regularization parameter. For reconstructing such an embedded structure by thermal waves the resolution turns out to be proportional to the depth and inversely proportional to the natural logarithm of the signal-to-noise ratio. This result could be derived from the diffusion equation by using a delta-source at a certain depth and setting the entropy production caused by thermal diffusion equal to the information loss. No specific model about the stochastic process of the fluctuations and about the distribution densities around the mean values was necessary to get this result.

cond-mat.stat-mech↗

arXiv2015

A Novel Compressed Sensing Scheme for Photoacoustic Tomography

Speeding up the data acquisition is one of the central aims to advance tomographic imaging. On the one hand, this reduces motion artifacts due to undesired movements, and on the other hand this decreases the examination time for the patient. In this article, we propose a new scheme for speeding up the data collection process in photoacoustic tomography. Our proposal is based on compressed sensing and reduces acquisition time and system costs while maintaining image quality. As measurement data we use random combinations of pressure values that we use to recover a complete set of pressure data prior to the actual image reconstruction. We obtain theoretical recovery guarantees for our compressed sensing scheme and support the theory by reconstruction results on simulated data as well as on experimental data.

math.NA↗

arXiv2013

Information loss, entropy production and time reversal for dissipative and diffuse processes

In non-destructive imaging the information about the spatial pattern of a samples interior has to be transferred to the sample surface by certain waves, e.g. ultrasound or electromagnetic waves. At the sample surface these waves can be detected and the interior structure is reconstructed from the measured signals. The amount of information about the interior of the sample, which can be gained from the detected waves on the sample surface, is essentially influenced by the propagation from its excitation to the surface. Scattering, dissipation, or diffusion causes entropy production and a loss of information for the propagating waves, and therefore results in a loss of resolution for imaging the interior structure. There have been made several attempts to compensate these diffusive or dissipative effects to get a higher resolution for the reconstructed images of the samples interior. In this work it is shown that thermodynamical fluctuations limit this compensation and therefore also the spatial resolution for non-destructive imaging at a certain depth is limited. We describe one example for diffusion and another one for dissipation and the loss of information is modeled by stochastic processes. For both examples the thermodynamic entropy production is equal to the loss of information, which results in a theoretical limit for the achievable spatial resolution in the reconstructed image.

cond-mat.stat-mech↗