Information theoretic perspective on sample complexity.

The statistical supervised learning framework assumes an input-output set with a joint probability distribution that is reliably represented by the training dataset. The learning system is then required to output a prediction rule learned from the training dataset's input-output pairs. In this work, we investigate the relationship between the sample complexity, the empirical risk and the generalization error based on the asymptotic equipartition property (AEP) (Shannon, 1948). We provide theoretical guarantees for reliable learning under the information-theoretic AEP, with respect to the generalization error and the sample size in different settings.

Domain-Aware Few-Shot Learning for Optical Coherence Tomography Noise Reduction.

Speckle noise has long been an extensively studied problem in medical imaging. In recent years, there have been significant advances in leveraging deep learning methods for noise reduction. Nevertheless, adaptation of supervised learning models to unseen domains remains a challenging problem. Specifically, deep neural networks (DNNs) trained for computational imaging tasks are vulnerable to changes in the acquisition system's physical parameters, such as: sampling space, resolution, and contrast. Even within the same acquisition system, performance degrades across datasets of different biological tissues. In this work, we propose a few-shot supervised learning framework for optical coherence tomography (OCT) noise reduction, that offers high-speed training (of the order of seconds) and requires only a single image, or part of an image, and a corresponding speckle-suppressed ground truth, for training. Furthermore, we formulate the domain shift problem for OCT diverse imaging systems and prove that the output resolution of a despeckling trained model is determined by the source domain resolution. We also provide possible remedies. We propose different practical implementations of our approach, verify and compare their applicability, robustness, and computational efficiency. Our results demonstrate the potential to improve sample complexity, generalization, and time efficiency, for coherent and non-coherent noise reduction via supervised learning models, that can also be leveraged for other real-time computer vision applications.