1. Spectrally Sparse Tensor Reconstruction in Optical Coherence Tomography Using Nuclear Norm Penalisation

    Spectrally Sparse Tensor Reconstruction in Optical Coherence Tomography Using Nuclear Norm Penalisation

    Reconstruction of 3D objects in various tomographic measurements is an important problem which can be naturally addressed within the mathematical framework of 3D tensors. In Optical Coherence Tomography, the reconstruction problem can be recast as a tensor completion problem. Following the seminal work of Candès et al., the approach followed in the present work is based on the assumption that the rank of the object to be reconstructed is naturally small, and we leverage this property by using a nuclear norm-type penalisation. In this paper, a detailed study of nuclear norm penalised reconstruction using the tubal Singular Value Decomposition ...

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