MeMGB-Diff: Memory-Efficient Multivariate Gaussian Bias Diffusion Model for 3D bias field correction

Bias fields inevitably degrade MRI that seriously interferes the diagnosis of physicians for accurate analysis, and removing it is a crucial image analysis task. Generative models (such as GANs) are used for bias field correction, and outperform traditional methods, however are hindered by the high cost of data annotation and instability during training. Recently, the diffusion-based methods have excelled over GANs in many applications, and they are powerful in removing noise from images, while the bias field can be regarded as a smooth noise. However, it is a challenge to directly apply to 3D bias field correction due to sampling inefficiency, the heavy computational demand, and implicit correction process. We propose a Memory-Efficient Multivariate Gaussian Bias Diffusion Model (MeMGB-Diff) that is an explicit, sampling, and memory both efficient diffusion model for 3D bias field correction without using clinical labels. MeMGB-Diff extends the diffusion models to multivariate Gaussian and models the bias field as a multivariate Gaussian variable, allowing direct diffusion and removal of the 3D bias fields without Gaussian noise. For memory efficiency, MeMGB-Diff performs diffusion model in smaller readable image domain at the expense of a negligible accuracy loss, based on the strong correlation among adjacent voxels of bias field. We also propose a loss function to mainly learn the intensity trend, which mainly causes the inhomogeneity of MRI, and effectively increases the correction accuracy. For comprehensive performance comparison, we propose a synthetic method for generating more varied bias fields during testing. Both quantitative and qualitative assessments on synthetic and clinical data confirm the high fidelity and uniform intensity of our results. MeMGB-Diff reduces data size by 64 times to use less memory, improves sampling efficiency by more than 10 times compared to other diffusion-based methods, and achieves optimal metrics, including SSIM, PSNR, COCO, and CV for various tissues. Hence, our MeMGB-Diff is a state-of-the-art (SOTA) method for 3D bias field correction.