Study on Quality Assessment Methods for Enhanced Resolution Graph-Based Reconstructed Images in 3D Capacitance Tomography  
[PERSON]  
1 Institute of Applied Computer Science, Lodz University of Technology, 18 Stefanowskiego Str., 90-537 Lodz, Poland 11 Institute of Information Technology, Lodz University of Technology, 8 Al. Politechniki Str., 93-590 Lodz, Poland 11 Institute of Applied Computer Science, Lodz University of Technology, 18 Stefanowskiego Str., 90-537 Lodz, Poland 11 Institute of Information Technology, Lodz University of Technology, 8 Al. Politechniki Str. nodes and edges. In the context of ECT image reconstruction, GNNs offer a novel approach to enhancing reconstruction quality. By representing the 3D finite element grid as a graph, where nodes correspond to grid vertices and edges encode spatial relationships, GCNs can effectively learn complex patterns within the data. This graph-based representation allows GCNs to capture intricate relationships between neighboring grid points and their associated electrical permittivity values. By leveraging this information, GCNs can refine the results of advanced non-linear reconstruction algorithms, such as those presented in [3], leading to more accurate and detailed ECT images. However, the recent integration of Graph Convolutional Networks into the reconstruction process of ECT images presents a new challenge, i.e., reconstructed image Quality Assessment. Traditional image quality metrics, designed for pixel-based data, struggle to effectively evaluate the reconstructed images represented as graphs. As highlighted in the seminal work by [PERSON] and [PERSON] [4], the need for objective image Quality Assessment methods has become paramount with the explosion of digital images and videos. This paper builds upon the established knowledge, acknowledging the limitations of existing methods when applied to the unique context of graph-based images in 3D ECT. The fundamental difference lies in the nature of the data. Classical image Quality Assessment thrives on the well-defined structure of raster images, where pixels form a predictable two-dimensional grid. In contrast, the structure of a graph-based image is far less rigid. Nodes, analogous to pixels, connect irregularly, making neighborhood relationships more complex and unpredictable. Another significant challenge arises from the shifting object problem. In 3D ECT scans, the reconstructed object might retain its shape across two images, but its position might differ slightly. This scenario renders direct comparisons between corresponding nodes ineffective. Even with perfect shape preservation, metrics like Mean Squared Error or Pearson Correlation Coefficient, which are simple but still prevalent in the field of ECT, can be significantly skewed by the object's shift. This highlights the need for a Quality Assessment method that remains insensitive to such positional variations. Furthermore, a robust metric is required to effectively compare different Graph Quality Assessment (GQA) methods. Ideally, this metric would involve comparing a Low-Quality (LQ) image, a High-Quality (HQ) image, and a reference phantom image (PH). A successful GQA method should consistently identify the higher degree of similarity between the HQ image and the PH image compared to the LQ and PH comparison. This approach allows for evaluating the GQA method's ability to accurately discern and quantify image quality differences. Therefore, this work proposes novel approaches specifically designed to address the Quality Assessment of graph-based ECT reconstructions. We leveraged existing QA methods while introducing new ideas to define several GQA methods. Simple methods that compare corresponding node values, such as Mean Squared Error (MSE), are straightforward to adapt because graph-based images are always compared with the same structure, differing only in node values. Thus, graph-based MSE simply compares the values of corresponding nodes in the compared images.