Neural Anisotropic Diffusion for MRI Denoising

Project Summary

The project treats Br35H brain MRI slices as a denoising benchmark. The model keeps the useful inductive bias of anisotropic diffusion, but learns the spatial conduction weights that control smoothing direction and strength.

Model

The denoiser computes local gradients across 4-neighbor or 8-neighbor stencils. A neural conduction network predicts per-direction diffusion coefficients, and an optional residual refinement stage improves the final reconstruction.

Evaluation

The final split uses 3000 images with 2100 training, 450 validation, and 450 test examples. Metrics include PSNR, SSIM, and Sobel edge MSE for boundary preservation.

Final Comparison

The learned PDE model substantially outperforms the classical denoising baselines. The plain U-Net baseline is included as a stronger neural comparison and achieves the best raw denoising metrics.

Method	PSNR	SSIM	Edge MSE
Noisy Input	17.711	0.425	0.194
Gaussian Smoothing	19.011	0.552	0.185
Median Filter	19.538	0.521	0.136
Bilateral Filter	18.955	0.463	0.136
Non-Local Means	20.393	0.585	0.087
Wavelet Denoising	19.519	0.530	0.106
Skimage TV	19.482	0.570	0.134
Curvature Flow	19.985	0.560	0.113
Classical PM	19.635	0.539	0.106
Unified Neural PDE	24.853	0.719	0.056
Plain U-Net Baseline	25.875	0.759	0.053

Higher PSNR and SSIM are better. Lower Edge MSE is better.

Interpreting The Results

The U-Net baseline performs best on raw denoising metrics, but that does not erase the value of the learned diffusion model. It clarifies what the project demonstrates.

What The Neural PDE Shows

The learned diffusion model beats every hand-designed denoising method in the benchmark by a large margin. Compared with Non-Local Means, it gains +4.460 dB PSNR and +0.134 SSIM while also reducing edge error.

That supports the core idea: a classical diffusion process becomes much stronger when the conduction behavior is learned from data.

What The U-Net Shows

The plain U-Net reaches 25.875 dB PSNR and 0.759 SSIM, outperforming the neural PDE model's 24.853 dB and 0.719 SSIM. It is the best black-box neural denoiser in the final run.

The honest takeaway is that the PDE model is more structured and interpretable, while the U-Net has more flexible representational power for this supervised denoising split.

The final claim is not that learned diffusion beats every neural architecture. The stronger conclusion is that it closes much of the gap between classical PDE denoising and modern neural denoisers while preserving an iterative diffusion structure.

Figures

The learned PDE model separates clearly from classical baselines, while the U-Net baseline is the strongest neural denoiser.

Representative clean, noisy, and denoised MRI slices.

Full Method Grid

Noise Robustness

Fixed-noise sweeps evaluate the trained PDE model across corruption types and strengths. Speckle noise is the easiest setting in this sweep; high Gaussian and high Rician corruption are the hardest.

Noise	Sigma 0.05	Sigma 0.10	Sigma 0.15	Sigma 0.20
Gaussian PSNR	26.376	24.567	22.655	21.063
Rician PSNR	26.669	25.536	24.513	22.094
Speckle PSNR	27.026	26.627	26.002	25.190
Mixed PSNR	26.699	25.600	24.407	22.765

Ablation Takeaways

The ablation suite indicates that residual refinement is the most important optional component. MiniUNet guidance did not help in the short ablation run.

Variant	PSNR	SSIM	Best Val Loss
Full Model	24.118	0.691	0.354
No MiniUNet Guidance	24.249	0.699	0.344
No Residual Refinement	22.798	0.601	0.443
4-Neighbor Diffusion	24.008	0.686	0.356