Optical coherence tomography (OCT) is a non-invasive imaging modality used for visualization of retinal tissue. However, OCT volumes are affected by speckle noise, which degrades image contrast and obscures fine structural details. Furthermore, modern clinical practice requires large field-of-view, high-resolution OCT volumes, whose storage and transmission are demanding for archiving and teleophthalmology applications. To address aforementioned challenges, we propose a low-rank multi-scale entanglement renormalization ansatz (MERA) tensor network approximation of 3D OCT image volume, where the image volume is represented as contractions of a top core factor encoding global features and multiple interacting low-rank orthogonal or semi-orthogonal factors modeling inter- and intra-B scan correlations. This representation jointly enables compression, denoising, and feature extraction. Unlike deep learning approaches, the proposed approach is training-free and processes each OCT volume independently. We evaluate the proposed framework on OCT image volumes acquired by two different scanners and demonstrate improved visual quality and reduced retinal layer segmentation errors in comparison with several competing methods. We also extract MERA features from two clinical OCT volume datasets. They are subsequently classified using a Grassmann-manifold nearest-subspace classifier. With the subspace dimension as its only hyperparameter, the classifier is theoretically shown to be robust in small-sample clinical scenario. We demonstrate competitive accuracy of classification of retinal diseases in these small-sample settings, where deep learning methods are often limited by the scarcity of labeled data. The proposed structure-aware model-driven representation learning for high-dimensional data under limited supervision provides good generalization performance while maintaining high interpretability.

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