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Karhunen-Loève Expansion-Based Residual Anomaly Map for Resource-Efficient Glioma MRI Segmentation

Anthony Hur

TL;DR

This work tackles the resource barrier in state-of-the-art brain tumor segmentation by integrating a discrete Karhunen–Loève expansion as a low-rank data model to generate a residual anomaly map from four-channel multi-modal MRI. The anomaly map is upsampled and used as a fifth input channel to a compact 3D U‑Net, enabling competitive BraTS-GLI 2023 performance on a consumer GPU with limited training data. On the validation set, the approach yields mean Dice scores of approximately $\text{WT}=0.929$, $\text{TC}=0.856$, and $\text{ET}=0.821$, with HD95 distances of $2.93$, $6.78$, and $10.35$ voxels, and even surpasses the winning method in HD95 while using far less computational power. The study demonstrates that grounded data reduction techniques like the discrete KL expansion can substantially reduce hardware and data requirements while preserving high segmentation performance, broadening accessibility for smaller labs and diverse datasets.

Abstract

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--Loève Expansion (KLE) was implemented as a feature extraction step on downsampled, z-score normalized MRI volumes. Each 240$\times$240$\times$155 multi-modal scan is reduced to four $48^3$ 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.

Karhunen-Loève Expansion-Based Residual Anomaly Map for Resource-Efficient Glioma MRI Segmentation

TL;DR

This work tackles the resource barrier in state-of-the-art brain tumor segmentation by integrating a discrete Karhunen–Loève expansion as a low-rank data model to generate a residual anomaly map from four-channel multi-modal MRI. The anomaly map is upsampled and used as a fifth input channel to a compact 3D U‑Net, enabling competitive BraTS-GLI 2023 performance on a consumer GPU with limited training data. On the validation set, the approach yields mean Dice scores of approximately , , and , with HD95 distances of , , and voxels, and even surpasses the winning method in HD95 while using far less computational power. The study demonstrates that grounded data reduction techniques like the discrete KL expansion can substantially reduce hardware and data requirements while preserving high segmentation performance, broadening accessibility for smaller labs and diverse datasets.

Abstract

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--Loève Expansion (KLE) was implemented as a feature extraction step on downsampled, z-score normalized MRI volumes. Each 240240155 multi-modal scan is reduced to four 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.
Paper Structure (22 sections, 7 equations, 7 figures)

This paper contains 22 sections, 7 equations, 7 figures.

Table of Contents

  1. Background
  2. Overview
  3. Literature Review
  4. Current Research 1: CNN-based BraTS segmentation
  5. Current Research 2: nnU-Net
  6. Current Research 3: Optimization and Loss Functions
  7. Current Research 4: KLE and anomaly-based data reduction
  8. Research Question
  9. Significance
  10. Academic Significance
  11. Technological Significance
  12. Research Hypothesis
  13. Materials and Methodology
  14. Prior Models
  15. Prior Mathematical Analysis
  16. ...and 7 more sections

Figures (7)

  • Figure 1: All four channels of a sample BraTS-GLI patient and the corresponding manual segmentation overlaid on the T1Gd image. From left to right: T1, T1Gd, FLAIR, T2, and T1Gd with label map (red = NCR/NET, yellow = ED, green = ET). Figure created by Anthony Joon Hur using Python.
  • Figure 2: Orthogonal axial, coronal, and sagittal FLAIR views with segmentation overlay for a representative BraTS-GLI case. Figure created by Anthony Joon Hur using Python.
  • Figure 3: Schematic representation of the 3D U-Net architecture used for BraTS segmentation. Dotted lines represent skip connections that concatenate encoder feature maps with decoder layers. Figure created by Anthony Joon Hur using LaTeX.
  • Figure 4: Flowchart of the proposed pipeline. The four MRI modalities are normalized and downsampled for KLE fitting, which produces a low-rank approximation and a residual-based anomaly map. The upsampled anomaly map is concatenated with the original modalities to form a 5-channel input for a 3D U-Net, which outputs the tumor segmentation. Figure created by Anthony Joon Hur using LaTeX.
  • Figure 5: Qualitative validation examples segmented by the proposed KLE-augmented 3D U-Net. Rows correspond to a lower-quartile case, a median case, and the best case according to the mean WT/TC/ET Dice on the validation crop. Columns display the FLAIR slice, the FLAIR slice with ground-truth labels, and the FLAIR slice with the predicted segmentation. Red = NCR/NET, yellow = ED, green = ET. Figure created by Anthony Joon Hur using Python.
  • ...and 2 more figures