Compressed Sensing Photoacoustic Tomography

The development of computerized tomography (CT) has revolutionized modern medical diagnostics. In the recent years several complementary tomographic modalities have been developed including x-ray CT, magnetic resonance imaging, single photon emission CT, or photoacoustic tomography (PAT). The unifying elements of these tomographic applications are that only indirect information about the quantity of interest can be collected when scanning the patient, and that mathematical reconstruction algorithms play an essential role for creating an image of the patient. A major aim in current CT research is reducing the number of measurements while preserving high contrast and resolution. This increases the speed of data acquisition, saves system costs, and can reduce radiation exposure. In this project we address these issues for PAT by developing, analyzing, and implementing novel compressed sensing techniques. PAT is a non-invasive biomedical imaging technology that beneficially combines the high contrast of pure optical imaging with the high spatial resolution of ultrasound imaging. It is based on the generation of acoustic waves by illuminating the patient or a specimen with short optical pulses. The induced acoustic waves are measured outside of the sample, and special reconstruction algorithms are used to recover a tomographic image of the patient or specimen. Using standard measurement designs, high-quality PAT requires collecting data with high sampling rate. However, each spatial measurement requires a separate sensor and high quality detectors are often costly. The compressed sensing techniques developed in this project allow to significantly reducing the number of measurements while preserving high image quality. The basic idea in compressed sensing is collecting special non-standard measurements in the form of random combinations of individual pressure values instead of sampling the pressure point-wise. Reconstructing high-resolution PAT images from such non-standard measurements requires the development of novel efficient reconstruction algorithms. In this project we develop compressed sensing techniques for PAT that (i) can be realizable in practice, (ii) come with an efficient numerical implementation, and (iii) are based on a solid mathematical fundament. We will realize our techniques experimentally by upgrading the existing photoacoustic imaging system, and develop and analyze efficient software tools for the novel PAT systems.

In this project, we developed innovative Compressed Sensing (CS) methods for Photoacoustic Tomography (PAT). PAT is an imaging technique similar to computed tomography, but produces a different type of image by imaging light-absorbing structures such as blood vessels. The main goal of CS is to develop special measurement tools to improve image quality while reducing the amount of data to be collected. We have successfully adapted and experimentally implemented this concept for PAT. Mathematical algorithms play a central role in the reconstruction of high quality PAT images from the CS data. We have successfully developed several such algorithms, in particular those based on deep learning and artificial intelligence. These achievements have relevance and potential applications not only for CS in PAT, but also in many tomographic applications. As two examples, we mention a wavelet decomposition for CSPAT, which inspired frame decompositions for general inverse problems. Furthermore, this project developed the first deep learning based image reconstruction methods for PAT.