Karhunen-Lo`eve Expansion-Based Residual Anomaly Map for Resource-Efficient Glioma MRI Segmentation

Accurate segmentation of brain tumors is essential for clinical diagnosis and treatment planning. Deep learning is currently the state-of-the-art for brain tumor segmentation, yet it requires either large datasets or extensive computational resources that are inaccessible in most areas. This makes the problem increasingly difficult: state-of-the-art models use thousands of training cases and vast computational power, where performance drops sharply when either is limited. The top performer in the Brats GLI 2023 competition relied on supercomputers trained on over 92,000 augmented MRI scans using an AMD EPYC 7402 CPU, six NVIDIA RTX 6000 GPUs (48GB VRAM each), and 1024GB of RAM over multiple weeks. To address this, the Karhunen--Lo`eve Expansion (KLE) was implemented as a feature extraction step on downsampled, z-score normalized MRI volumes. Each 240×240×155 multi-modal scan is reduced to four 483 channels and compressed into 32 KL coefficients. The resulting approximate reconstruction enables a residual-based anomaly map, which is upsampled and added as a fifth channel to a compact 3D U-Net. All experiments were run on a consumer workstation (AMD Ryzen 5 7600X CPU, RTX 4060Ti (8GB VRAM), and 64GB RAM while using far fewer training cases. This model achieves post-processed Dice scores of 0.929 (WT), 0.856 (TC), and 0.821 (ET), with HD95 distances of 2.93, 6.78, and 10.35 voxels. These results are significantly better than the winning BraTS 2023 methodology for HD95 distances and WT dice scores. This demonstrates that a KLE-based residual anomaly map can dramatically reduce computational cost and data requirements while retaining state-of-the-art performance.