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e-Journal of Nondestructive Testing

Volumetric Denoising of XCT Data Using Quantum Computing

Thomas Lang, Anja Heim, Anastasia Papadaki, Kilian Dremel, Dimitri Prjamkov, Martin Blaimer, Markus Firsching, Stefan Kasperl, Theobald O. J. Fuchs

Published Jan 30, 2025• 1 citation
Publisher

Abstract

Quantum computing is an emerging field of technology that utilizes unique properties such as the superposition principle and quantum entanglement, potentially enabling the development of techniques that are drastically faster or even the only feasible solutions compared to classical approaches. Thus, it promises enormous gains in several domains, including the processing of n-dimensional images, such as those produced by X-ray computed tomography. However, the latter is subject to physical effects that primarily include artifacts and quantum noise. Noise, in particular, is an unavoidable issue that needs to be addressed when processing X-ray data. Therefore, this work considers the denoising of 3D volumetric data using quantum computing. An adaptation of a mathematical denoising model was transformed to be suitable for quantum implementation, and preliminary experiments demonstrated its functionality with two-dimensional images. Here, we first lift this model to be applicable to 3D images. Next, we provide an implementation in form of quantum circuits and consider issues of a practical implementation occurring specifically in 3D. The final implementation is executed on a real X-ray computed tomography dataset, showing that proper denoising can be performed on quantum devices, yet current technological limitations inhibit the application to large datasets.

DOI
10.58286/30732

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Quantum computing is an emerging field of technology that utilizes unique properties such as the superposition principle and quantum entanglement, potentially enabling the development of techniques that are drastically faster or even the only feasible solutions compared to classical approaches. Thus, it promises enormous gains in several domains, including the processing of n-dimensional images, such as those produced by X-ray computed tomography. However, the latter is subject to physical effects that primarily include artifacts and quantum noise. Noise, in particular, is an unavoidable issue that needs to be addressed when processing X-ray data. Therefore, this work considers the denoising of 3D volumetric data using quantum computing. An adaptation of a mathematical denoising model was transformed to be suitable for quantum implementation, and preliminary experiments demonstrated its functionality with two-dimensional images. Here, we first lift this model to be applicable to 3D images. Next, we provide an implementation in form of quantum circuits and consider issues of a practical implementation occurring specifically in 3D. The final implementation is executed on a real X-ray computed tomography dataset, showing that proper denoising can be performed on quantum devices, yet current technological limitations inhibit the application to large datasets.
Quantum computing is currently one of the fastest emerging branches of information processing due to its theoretical computation powers exceeding conventional computers by far. However, currently well-known quantum-powered algorithms are of theoretical nature and its effect on practical problems has yet to be discovered. This work reviews current approaches in context of the applicability of quantum computing for the domain of image processing with respect to 3D computed tomography. It focuses on the encoding of n-dimensional images on a quantum computer and also the quantum measurement process, i.e., the image read-out. First results show that while the encoding is indeed highly efficient and is well-suited for representing 3D voxel data as obtained from computed tomography, the decoding to a classical representation is rather expensive. The latter part is also very sensitive to quantum hardware noise as was evidenced by both noisy simulator and real quantum hardware experiments.
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Quantum Image Processing (QIP) is a field that aims to utilize the benefits of quantum computing for manipulating and analyzing images. However, QIP faces two challenges: the limitation of qubits and the presence of noise in a quantum machine. In this research, we propose a novel approach to address the issue of noise in QIP. By training and employing a machine learning model that identifies and corrects the noise in quantum-processed images, we can compensate for the noisiness caused by the machine and retrieve a processing result similar to that performed by a classical computer with higher efficiency. The model is trained by learning a dataset consisting of both existing processed images and quantum-processed images from open-access datasets. This model will be capable of providing us with the confidence level for each pixel and its potential original value. To assess the model's accuracy in compensating for loss and decoherence in QIP, we evaluate it using three metrics: Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Mean Opinion Score (MOS). Additionally, we discuss the applicability of our model across domains well as its cost effectiveness compared to alternative methods.
Quantum Image Processing (QIP) is a field that aims to utilize the benefits of quantum computing for manipulating and analyzing images. However, QIP faces two challenges: the limitation of qubits and the presence of noise in a quantum machine. In this research we propose a novel approach to address the issue of noise in QIP. By training and employing a machine learning model that identifies and corrects the noise in quantum processed images, we can compensate for the noisiness caused by the machine and retrieve a processing result similar to that performed by a classical computer with higher efficiency. The model is trained by learning a dataset consisting of both existing processed images and quantum processed images from open access datasets. This model will be capable of providing us with the confidence level for each pixel and its potential original value. To assess the model's accuracy in compensating for loss and decoherence in QIP, we evaluate it using three metrics: Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Mean Opinion Score (MOS). Additionally, we discuss the applicability of our model across domains well as its cost effectiveness compared to alternative methods.
One of the primary difficulties in computed tomography (CT) is reconstructing cross-sectional images from measured projections of a physical object. There exist several classical methods for this task of generating a digital representation of the object, including filtered backprojection or simultaneous algebraic reconstruction technique. Our research aims to explore the potential of quantum computing in the field of industrial X-ray transmission tomography. Specifically, this work focuses on the application of a method similar to that proposed by Nau et al. (2023) on real CT data to demonstrate the feasibility of quadratic-unconstrained-binary-optimization-based tomographic reconstruction. Starting with simulated phantoms, results with simulated annealing as well as real annealing hardware are shown, leading to the application on measured cone-beam CT data. The results demonstrate that tomographic reconstruction using quantum annealing is feasible for both simulated and real-world applications. Yet, current limitations—involving the maximum processable size and bit depth of voxel values of the images, both correlated with the number of densely connected qubits within the annealing hardware—imply the need of future research to further improve the results. This approach, despite its early stage, has the potential to enable more sophisticated reconstructions, providing an alternative to traditional classical methods.
This contribution will sum-up the current state of Quantum Computing and give a short overview of the theoretical background. The concept of qubits, superposition, entanglement and measurement of quantum states will be explained. In particular the interaction of multiple quantum objects lead to highly complex combined states, represented by high-dimensional matrices. Quantum gates and circuits built from these gates will be introduced. Next, we will report on the current state of our research on several applications of QC. These include an implementation of cross-sectional image reconstruction for CT imaging based on a QUBO-method (Quadratic Unconstrained Binary Optimization), used to find a mathematical minimum of a metric. Another topic, we are working on, is optimization of X-ray source trajectory in CT with respect to image quality achievable by a restricted number of angular positions. In addition, we evaluate various encoding techniques for images. Based on that we examine common problems of image processing for instance noise reduction and search for ways to implement respective methods on the QC.