A Quantum-Inspired Self-Supervised Network model for automatic segmentation of brain MR images
Graphical abstract
Introduction
The unified concept of quantum information processing explores a new emerging field of research in computer science, referred to as quantum-inspired computing [1], [2], [3]. Conventionally, a plethora of quantum-inspired neural networks (QINN) are evolved over the years targeted to solve pattern recognition and classification problems [4], [5], [6], [7], [8] using the inherent characteristics offered by quantum mechanics. However, these quantum-inspired neural network models are supervised in nature and rely on complex and time consuming quantum back-propagation algorithms. In addition, the QINN models employ fixed thresholding for the activation function and hence are not applicable for the gray-scale images with wide variation of gray levels.
Magnetic Resonance Imaging (MRI) is a non-invasive technology which allows to acquire and investigate structural images including tumors. The Brain tumor diagnosis essentially requires the key information prevalence to the shape, size, location and metabolism of brain tumors. However, it is always a daunting task for the radiologists to segment tumor regions and to distinguish various typical brain tumors owing to wide variation in shape, orientation, intensity in-homogeneity and overlapping in the spatial imaging plane. In these circumstances, development of a robust and automated computational technique suitable for MR image segmentation and tumor regions detection received much attention among the computer vision research community. Brain tumor segmentation procedure comprises diagnosing, delineating and isolating tumor tissues from healthy brain tissues.
The primary focus of the suggested work is to propose a new pattern identification integrated self-supervised framework abbreviated as QIS-Net and it is characterized by Quantum-inspired Multi-level Sigmoidal (QMSig) activation function applicable for fully automated segmentation of brain tumors without any external supervision. The proposed QIS-Net architecture rely on a novel quantum-inspired neural model and resorted to self-supervised procedure guided by counter propagation of the network states to obviate complex quantum back-propagation algorithm employed in supervised QINN models. The key thresholding aspect behind the suggested QIS-Net is induced by the spread of intensity in underlying images in an adaptive fashion. Various thresholding schemes have been reported in this article encompassing image context sensitive thresholding in quantum environments. The hyper parameters pertaining to the thresholding process are adaptive in nature and depend on image pixel intensity. It may be noted that the proposed quantum-inspired self-supervised architecture is implemented on a classical computer relying on quantum neuron models and procedures [4], [8], [9], [10] and hence the suggested model architecture is refereed to as quantum-inspired self-supervised neural network (QIS-Net) instead of quantum self-supervised neural network architecture. The major contributions of the manuscript are as follows.
- 1.
In this work, the standard bi-level sigmoidal activation function employed in our previous work (QBDSONN architecture) [9], [10] has been extended to a novel Quantum Inspired Multi-level Sigmoid activation (QMSig) function to address the gray level heterogeneity pertaining to images.
- 2.
Our self-supervised QIS-Net resorts to a functional modification instead of replicating the identical network architecture for each gray level by introducing a novel quantum-inspired network model characterized by a quantum-inspired multi-level sigmoidal activation function (QMSig) thereby cutting down both space and time complexities.
- 3.
The suggested quantum-inspired self-supervised neural network model embedded in the QIS-Net architecture relies on invoking imaginary section of the quantum information processing which is the major distinction with the QIBDS Net [11] for Brain MR image segmentation. Hence, the present attempt tries to explore the inherent quantum correlations thereby yielding faster convergence of the network architecture.
- 4.
The incorporation of quantum computing provides better convergence of the proposed QIS-Net architecture by means of incorporating the frequency components of the interconnection weights and the network inputs thereby enabling faster convergence of the network states in addition to fast and accurate MR image segmentation outcome.
The suggested QIS-Net architecture is applicable for any gray scale image segmentation and the outcome is subject to investigation. However, in this paper, the hyper-parameters of current network architecture are tailored solely for the application of brain MR image segmentation. Rigorous experiments have been carried out on large Nature data sets of images [12].
The remaining portion of the report is organized as follows: an in-depth review of the relevant methods for brain MR image segmentation has been discussed in Section 2. This section also elucidates the focus area of research with motivation. The basic concepts of quantum computing are illustrated in Section 3. A short description about the suggested QIS-Net architecture with novel quantum-inspired neural model and Quantum-inspired Multi-level Sigmoidal (QMSig) activation function has been elaborated in Section 4. Section 5 sheds light MR image segmentation using the proposed quantum-inspired self-supervised architecture. Results and discussions are reflected in Section 6. Finally, remarks about conclusion and future work are presented in Section 7.
Section snippets
Literature review
Artificial Neural Networks (ANN) based frameworks for MR image segmentation received great attention owing to their parallel and adaptive computing capabilities [13], [14]. Notable examples include the fuzzy logic inspired ANN for MR image segmentation [15], [16], [17]. Kumar et al. introduced a multi-class Artificial Neural Network (ANN) classifier applied to MR images segmentation with dimensionality reduction through Principal Component Analysis (PCA) [14]. A Self-Organizing Feature Map
Fundamentals of quantum computing
The basic principles of quantum mechanics offer to create computational devices capable of implementing quantum computing algorithms. Quantum mechanical operations like superposition, coherence, decoherence, entanglement [36] are employed to characterize the basic states of quantum computing and it is referred to as qbits or quantum bits.
Quantum-inspired self-supervised network (QIS-Net) architecture
The QIS-Net architecture is composed of trinity layers of quantum neurons and arranged as input, hidden and output layers described qbits. A simplified diagram of QIS-Net architecture is illustrated in Fig. 1.
The input layer of the QIS-Net architecture acts as a gateway and transfers normalized image information to the successive intermediate and output layers for further processing. The image pixels are fed to the input layer as quantum bits and propagates from the input to intermediate layer
MR image segmentation using the proposed QIS-Net
The proposed QIS-Net receives the input MR image pixel information and it transforms the fuzzified information with various gray scales into quantum phase [, ] as The fixed activation parameter employed in the quantum inspired multi-level sigmoidal (QMSig) activation function is suitable for uniformly distributed intensity images. However, due to wide variations of gray levels in image pixels, MR images exhibits heterogeneous responses over the -connected neighborhoods. Hence,
Data set
Dynamic Susceptibility Contrast (DSC) MR image segmentation for brain tumor detection is performed using QIS-Net characterized by the suggested quantum-inspired network model with QMSig activation function. The Dynamic Susceptibility Contrast (DSC) brain MR images are collected from Nature data sets [12]. The proposed quantum-inspired self-supervised procedure using QIS-Net with adaptive thresholding schemes, the unsupervised fuzzy-C-means clustering (FCM) [17] and the self-supervised network
Conclusion
In this article, a Quantum-Inspired Self-Supervised Network (QIS-Net) architecture characterized by QMSig activation function has been proposed to promote fully automatic segmentation of Dynamic Susceptibility Contrast (DSC) brain MR images in real-time. The incorporation of quantum computing aims at providing better convergence of the QIS-Net resulting in fast and accurate MR image segmentation. The proposed quantum-inspired self-supervised procedure is the first novel attempt involving any
CRediT authorship contribution statement
Debanjan Konar: Conceptualization, Methodology, Software, Investigation, Validation, Writing - original draft. Siddhartha Bhattacharyya: Data curation, Writing - review & editing, Supervision. Tapan Kr. Gandhi: Supervision. Bijaya Ketan Panigrahi: Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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