A FourierKAN-Enhanced GraphSAGE Model with a Linear Compressed Variational Quantum Circuit for Residual Correction in Brain Tumor Segmentation

Accurate brain tumor segmentation from multimodal magnetic resonance imaging (MRI) remains challenging because of dissimilar tumor appearance and irregular spatial structure. This study proposes FKAN-GSAGE-LVQC, a hybrid segmentation framework integrating FourierKAN-based feature enhancement, GraphSAGE spatial aggregation, and a linear compressed variational quantum circuit (VQC) residual branch. MRI-derived regions are represented as graphs using 12-dimensional node features. FourierKAN enhances node representations, while a three-layer GraphSAGE backbone aggregates spatial information. A four-qubit VQC generates residual corrections to the classical node-level predictions, and an MRI-conditioned voxel decoder further refines the voxel-wise probabilities reconstructed from graph predictions. Experiments were conducted using 1251 labeled BraTS2021 subjects, divided at the patient level into 876 training, 125 validation, and 250 internal held-out test subjects. On the independent internal test cohort, the proposed framework achieved a mean Dice of 0.840412±0.001501 across three independent graph-model training seeds, with WT, TC, and ET Dice scores of 0.9079, 0.8228, and 0.7905, respectively. The reported mean HD95 was 6.6904 mm. Compared with a parameter-matched classical residual control, the proposed configuration improved mean Dice by 0.009182. Furthermore, it achieved the highest mean Dice among seven models evaluated under the common experimental protocol. These results demonstrate competitive segmentation performance on the internal held-out test cohort, while the specific contribution of the trainable VQC is assessed through controlled comparisons.