Peter Burgholzer

Michael Sandbichler, Felix Krahmer, Thomas Berer et al.

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.

Markus Haltmeier, Michael Sandbichler, Thomas Berer et al.

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.

Benjamin Walder, Daniel Toader, Robert Nuster et al.

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.

Markus Haltmeier, Matthias Ye, Karoline Felbermayer et al.

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.

Markus Haltmeier, Thomas Berer, Sunghwan Moon et al.

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.