Backward Stochastic Differential Equations-guided Generative Model for Structural-to-functional Neuroimage Translator

TL;DR

This work tackles structural-to-functional neuroimage translation by introducing a Backward Stochastic Differential Equations (BSDE) guided generative model (BGM). It builds on the nonlinear Feynman-Kac link between BSDEs and PDEs to design a forward process $X_t$ and backward process $Y_t$, with $X_0=\zeta$ from multimodal inputs and $Y_T=\xi$ matching the target CBV distribution, enabling CBV synthesis from standard MRI sequences. The approach is evaluated against GAN-based and Pix2Pix/Encoder-Decoder baselines on CBV, DWI, and T1C generation tasks, showing superior metrics such as LPIPS, MAE, MSE, PSNR, and SSIM in various settings. By coupling stochastic dynamics with principled boundary-conditioned posteriors and an analytic posterior under certain boundary conditions, the paper advances robust, theoretically grounded structural-to-functional neuroimaging translation with potential clinical impact.

Abstract

A Method for structural-to-functional neuroimage translator

Figures (1)

• Figure 1: Flowchart for synthesizing cerebral blood volume (CBV) maps from standard MRI sequences using BGM.