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This paper proposes low tensor-train (TT) rank and low multilinear (ML) rankapproximations for de-speckling and compression of 3D optical coherencetomography (OCT) images for a given compression ratio (CR). To this end, wederive the alternating direction method of multipliers based algorithms for therelated problems constrained with the low TT- and low ML rank. Rank constraintsare implemented through the Schatten-p (Sp) norm, p e {0, 1/2, 2/3, 1}, ofunfolded matrices. We provide the proofs of global convergence towards astationary point for both algorithms. Rank adjusted 3D OCT image tensors arefinally approximated through tensor train- and Tucker alternating least squaresdecompositions. We comparatively validate the low TT- and low ML rank methodson twenty-two 3D OCT images with the JPEG2000 and 3D SPIHT compression methods,as well as with no compression 2D bilateral filtering (BF), 2D median filtering(MF), and enhanced low-rank plus sparse matrix decomposition (ELRpSD) methods.For the CR<10, the low Sp TT rank method with pe{0, 1/2, 2/3} yields eitherhighest or comparable signal-to-noise ratio (SNR), and comparable or bettercontrast-to-noise ratio (CNR), mean segmentation errors (SEs) of retina layersand expert-based image quality score (EIQS) than original image and imagecompression methods. It compares favorably in terms of CNR, fairly in terms ofSE and EIQS with the no image compression methods. Thus, for CR<10 the low S2/3TT rank approximation can be considered a good choice for visual inspectionbased diagnostics. For 2<CR<60, the low S1 ML rank method compares favorably interms of SE with image compression methods and with 2D BF and ELRpSD. It isslightly inferior to 2D MF. Thus, for 2<CR<60, the low S1 ML rank approximationcan be considered a good choice for segmentation based diagnostics eitheron-site or in the remote mode of operation.

Low Tensor Train- and Low Multilinear Rank Approximations for De-speckling and Compression of 3D Optical Coherence Tomography Images