Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*) or magnetisation-transfer saturation (MTsat), involves inverting a highly non-linear function. Many methods for deriving parameter maps assume perfect measurements and do not consider how noise is propagated through the estimation procedure, resulting in needlessly noisy maps. Instead, we propose a probabilistic generative (forward) model of the entire dataset, which is formulated and inverted to jointly recover (log) parameter maps with a well-defined probabilistic interpretation (e.g., maximum likelihood or maximum a posteriori). The second order optimisation we propose for model fitting achieves rapid and stable convergence thanks to a novel approximate Hessian. We demonstrate the utility of our flexible framework in the context of recovering more accurate maps from data acquired using the popular multi-parameter mapping protocol. We also show how to incorporate a joint total variation prior to further decrease the noise in the maps, noting that the probabilistic formulation allows the uncertainty on the recovered parameter maps to be estimated. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.
翻译:量化的MMS成像因其信息内容丰富和标准化措施而越来越偏好。然而,计算定量参数图,如编码的纵向放松率(R1)、明显的反向放松率(R2*)或磁性转移饱和度(MTsat),需要翻转一个高度非线性功能。许多测算参数图的方法是完美的测量,不考虑如何通过估计程序传播噪音,从而导致不必要的吵闹地图。相反,我们建议对整个数据集采用一种概率化(向前)模型,该模型的编制和反向是联合恢复(log)参数图,并配有明确界定的概率性解释(例如,最大的可能性或最大的可能性);我们提议的模型安装的第二顺序优化由于新颖的海珊近度而迅速和稳定地趋同。我们展示了我们灵活框架在从使用流行的多参数绘图协议获得的数据中恢复更准确的地图的效用。我们还表明,在进一步减少地图的噪音之前,如何将联合全面变换成(log)参数图(例如,事后解释(例如,最大的可能性)或最大)。我们提议的模型的加速化方法可以使我们的加速化的进度图得到利用。