This paper introduces a novel shallow 3D self-supervised tensor neural network for volumetric segmentation of medical images with merits of obviating training and supervision. The proposed network is referred to as 3D Quantum-inspired Self-supervised Tensor Neural Network (3D-QNet). The underlying architecture of 3D-QNet is composed of a trinity of volumetric layers viz. input, intermediate and output layers inter-connected using an S-connected third-order neighborhood-based topology for voxel-wise processing of 3D medical image data suitable for semantic segmentation. Each of the volumetric layers contains quantum neurons designated by qubits or quantum bits. The incorporation of tensor decomposition in quantum formalism leads to faster convergence of the network operations to preclude the inherent slow convergence problems faced by the classical supervised and self-supervised networks. The segmented volumes are obtained once the network converges. The suggested 3D-QNet is tailored and tested on the BRATS 2019 Brain MR image data set and Liver Tumor Segmentation Challenge (LiTS17) data set extensively in our experiments. 3D-QNet has achieved promising dice similarity as compared to the intensively supervised convolutional network-based models like 3D-UNet, Vox-ResNet, DRINet, and 3D-ESPNet, showing a potential advantage of our self-supervised shallow network on facilitating semantic segmentation.

The slow-convergence problem degrades the segmentation performance of the recently proposed Quantum-Inspired Self-supervised Neural Network models owing to lack of suitable tailoring of the inter-connection weights. Hence, incorporation of quantum-inspired meta-heuristics in the Quantum-Inspired Self-supervised Neural Network models optimizes their hyper-parameters and inter-connection weights. This paper is aimed at proposing an optimized version of a Quantum-Inspired Self-supervised Neural Network (QIS-Net) model for optimal segmentation of brain Magnetic Resonance (MR) Imaging. The suggested Optimized Quantum-Inspired Self-supervised Neural Network (Opti-QISNet) model resembles the architecture of QIS-Net and its operations are leveraged to obtain optimal segmentation outcome. The optimized activation function employed in the presented model is referred to as Quantum-Inspired Optimized Multi-Level Sigmoidal (Opti-QSig) activation. The Opti-QSig activation function is optimized by three quantum-inspired meta-heuristics with fifitness evaluation using Otsu’s multi-level thresholding. Rigorous experiments have been conducted on Dynamic Susceptibility Contrast (DSC) brain MR images from Nature data repository. The experimental outcomes show that the proposed self-supervised Opti-QISNet model offffers a promising alternative to the deeply supervised neural network based architectures (UNet and FCNNs) in medical image segmentation and outperforms our recently developed models QIBDS Net and QIS-Net.