The application of deep neural networks (DNNs) is revolutionizing numerous scientific and engineering fields, with a significant impact on imaging. Traditional image-reconstruction algorithms are now being outperformed by DNN-based techniques, both qualitatively and quantitatively. This shift opens new opportunities to extend the capabilities of existing imaging infrastructure. Specifically, DNNs can improve signal-to-noise ratios, enhance image resolution, and enable image reconstruction from fewer measurements (compressed sensing), which leads to faster imaging and reduced radiation doses for patients.
However, while these advancements are promising, caution is needed. The inner workings of DNNs remain poorly understood, while top-performing reconstruction algorithms often show vulnerabilities such as a reduced robustness and a propensity to generate so-called hallucinations. We attribute this behavior to their inherent instability. The latter can be quantified through the Lipschitz constant of the network, which measures the degree to which small input perturbations can cause significant output deviations.
In the FunLearn project, we aim to leverage advanced machine learning to push the frontiers of bioimaging, while ensuring the reliability and trustworthiness of our methods. To reach our goal, we therefore first need to develop safer computational architectures. While the Lipschitz constant of a deep neural network can be controlled in a layer-wise fashion, such a control negatively affects expressivity and, hence, performance. Since the effect worsens with depth, our solution is to rely on shallow neural architectures which are easier to control. Moreover, we can enhance their expressivity by increasing the sophistication of the layers, for instance by including learnable activations as alternatives to the fixed units (ReLU) of conventional networks or by considering higher-dimensional trainable nonlinearities.
Our main objectives are thus: (i) to develop novel, more robust learning architectures based on functional-optimization methods; and (ii) to apply these tools to address significant challenges in biomedical imaging.
