Medical Image Analysis Project

Neural Anisotropic Diffusion for MRI Denoising

A learned variant of the Perona-Malik diffusion process that unrolls a PDE into a neural network to achieve edge-preserving smoothing in brain MRI scans.

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24.85 dB Neural PDE PSNR
0.719 Neural PDE SSIM
+4.46 dB Gain vs. NLM Baseline
16 Iter Unrolled PDE Steps

Project Abstract

This project presents a novel, learned variant of the Perona-Malik anisotropic diffusion process. By unrolling the classical Partial Differential Equation (PDE) into a neural network architecture, we replace hand-designed conduction functions with a spatially-adaptive conduction network. Our model incorporates a MiniUNet guidance encoder and an 8-neighbor diffusion mode to effectively suppress noise while preserving critical anatomical edges. Evaluated on the Br35H dataset, our Unified Neural PDE model achieved a PSNR of 24.85 dB, outperforming the best classical baseline by +4.46 dB.

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Methodology

Neural PDE Architecture

The model unrolls the diffusion process into iterative steps. At each step, a Conduction Network predicts spatially varying diffusion weights for 8 neighboring pixels.

A MiniUNet guidance encoder provides global context to the diffusion process, while a final residual refinement stage recovers fine details smoothed by the PDE.

Updated architecture diagram for the unified neural PDE model.

Unified neural anisotropic diffusion architecture diagram

Hybrid Loss Function

The model is trained using a composite loss that prioritizes both structural fidelity and edge sharpess.

  • SSIM Loss: Preserves global structural similarity.
  • L1 Loss: Ensures pixel-level fidelity.
  • Gradient Loss: Penalizes blurring of anatomical boundaries.

The Gradient loss is critical for ensuring the denoiser doesn't wash out small lesion margins or cortical edges.

Qualitative Analysis

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Multi-Method Comparison

Visualizing the denoising performance across classical filters and neural approaches. Our model (Neural PDE) preserves contrast and edges significantly better than the hand-designed baselines.

Discussion & Conclusion

Interpretability

Unlike "black-box" CNNs, our model follows a physical diffusion process. By inspecting the conduction weights, we can verify that the model is intelligently stopping diffusion at detected edges, matching the inductive bias of classical medical imaging.

Conclusion

The project demonstrates that learned anisotropic diffusion bridges the gap between classical PDEs and deep learning. It achieves massive gains over traditional filters (+4.4 dB PSNR) while remaining structured and interpretable.