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Purpose. To develop a method that can reduce and estimate uncertainty in quantitative MR parameter maps without the need for hand-tuning of any hyperparameters.

Methods. We present an estimation method where uncertainties are reduced by incorporating information on spatial correlations between neighbouring voxels. The method is based on a Bayesian hierarchical non-linear regression model, where the parameters of interest are sampled, using Markov chain Monte Carlo (MCMC), from a high-dimensional posterior distribution with a spatial prior. The degree to which the prior affects the model is determined by an automatic hyperparameter search using an information criterion and is, therefore, free from manual user-dependent tuning. The samples obtained further provide a convenient means to obtain uncertainties in both voxels and regions. The developed method was evaluated on T₁ estimations based on the variable flip angle method.

Results. The proposed method delivers noise-reduced T₁ parameter maps with associated error estimates by combining MCMC sampling, the widely applicable information criterion, and total variation-based denoising. The proposed method results in an overall decrease in estimation error when compared to conventional voxel-wise maximum likelihood estimation. However, this comes with an increased bias in some regions, predominately at tissue interfaces, as well as an increase in computational time.

Conclusions. This study provides a method that generates more precise estimates compared to the conventional method, without incorporating user subjectivity, and with the added benefit of uncertainty estimation.

Purpose: To mitigate the problem of noisy parameter maps with high uncertainties by casting parameter mapping as a denoising task based on Deep Image Priors.

Methods: We extend the concept of denoising with Deep Image Prior (DIP) into parameter mapping by treating the output of an image-generating network as a parametrization of tissue parameter maps. The method implicitly denoises the parameter mapping process by filtering low-level image features with an untrained convolutional neural network (CNN). Our implementation includes uncertainty estimation from Bernoulli approximate variational inference, implemented with MC dropout, which provides model uncertainty in each voxel of the denoised parameter maps. The method is modular, so the specifics of different applications (e.g., T1 mapping) separate into application-specific signal equation blocks. We evaluate the method on variable flip angle T1 mapping, multi-echo T2 mapping, and apparent diffusion coefficient mapping.

Results: We found that deep image prior adapts successfully to several applications in parameter mapping. In all evaluations, the method produces noise-reduced parameter maps with decreased uncertainty compared to conventional methods. The downsides of the proposed method are the long computational time and the introduction of some bias from the denoising prior.

Conclusion: DIP successfully denoise the parameter mapping process and applies to several applications with limited hyperparameter tuning. Further, it is easy to implement since DIP methods do not use network training data. Although time-consuming, uncertainty information from MC dropout makes the method more robust and provides useful information when properly calibrated.

Purpose: To make Deep Image Prior (DIP)-based parameter mapping faster, more accurate, and suitable for clinical applications, with added support for multislice and 3D datasets.

Methods: DIP leverages the inherent structure of an untrained image generator to address various inverse imaging tasks, including denoising. In this study, we enhance DIP-based denoising for parameter mapping with warm-start across neighboring image slices and different patient subjects. This approach leverages spatial similarity to reduce computation time. Additionally, we introduce an early-stopping criterion that selects the denoising level based on MRI signal noise. We further investigate uncertainty calibration through dropout probability tuning to address issues with miscalibrated uncertainty estimates from Monte Carlo dropout. Furthermore, we explore reducing computation time by tuning learning rates and network complexity.

Results: We show that reusing image generator weights with warm-start significantly accelerates the denoising of large datasets, reducing computation time by 78% to 95% across various tasks. The early stopping approach proved effective, eliminating the need to manually select the number of optimization steps. Dropout probability tuning helps mitigate the issue of miscalibrated uncertainty, though further refinements are necessary, particularly to achieve better calibration on a per-pixel level. Additionally, tuning learning rates and network complexity provided valuable insights into optimizing the model for different tasks.

Conclusion: The proposed developments enable DIP-based parameter mapping to become faster, more accurate, and, consequently, more practical and scalable for clinical applications involving larger datasets.