Apparent Ultra-High $b$-Value Diffusion-Weighted Image Reconstruction via Hidden Conditional Random Fields

A promising, recently explored, alternative to ultra-high b-value diffusion weighted imaging (UHB-DWI) is apparent ultra-high b-value diffusion-weighted image reconstruction (AUHB-DWR), where a computational model is used to assist in the reconstruction of apparent DW images at ultra-high b-values. Firstly, we present a novel approach to AUHB-DWR that aims to improve image quality. We formulate the reconstruction of an apparent DW image as a hidden conditional random field (HCRF) in which tissue model diffusion parameters act as hidden states in this random field. The second contribution of this paper is a new generation of fully connected conditional random fields, called the hidden stochastically fully connected conditional random fields (HSFCRF) that allows for efficient inference with significantly reduced computational complexity via stochastic clique structures. The proposed AUHB-DWR algorithms, HCRF and HSFCRF, are evaluated quantitatively in nine different patient cases using Fisher's criteria, probability of error, and coefficient of variation metrics to validate its effectiveness for the purpose of improving intensity delineation between expert identified suspected cancerous and healthy tissue within the prostate gland. The proposed methods are also examined using a prostate phantom, where the apparent ultra-high b-value DW images reconstructed using the tested AUHB-DWR methods are compared with real captured UHB-DWI. The results illustrate that the proposed AUHB-DWR methods has improved reconstruction quality and improved intensity delineation compared with existing AUHB-DWR approaches.