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Quantitative magnetic resonance imaging (qMRI) is a subset of MRI that moves beyond qualitative image interpretation towards more objective and reproducible quantification of tissue parameters, a process referred to as parameter mapping. In cancer imaging, this capability has the potential to assist with characterizing tumors, monitoring treatment response, and comparing scans both over time and across different scanners or imaging sites. This thesis addresses the problem of uncertainty in parameter mapping. This is done by developing methods that both reduce uncertainty and estimate the uncertainty that remains, two important components for advancing the clinical reliability of qMRI. The first component, reducing uncertainty, focuses on reducing noise in the parameter maps. In this thesis, we propose methods that apply denoising priors to stabilize the parameter mapping process. The second component, estimating the remaining uncertainty, aims to quantify what uncertainty remains after denoising has been applied. This is achieved through uncertainty estimation, providing a more complete picture of the results.

Paper I presents a method for T1 mapping that combines an explicit denoising prior, in the form of total variation (TV) regularization, together with uncertainty estimation using Markov chain Monte Carlo (MCMC) sampling. The strength of the TV prior is selected in a data-driven way which reduces the requirement of manual tuning. This approach produces denoised parameter maps with reduced uncertainty and meaningful uncertainty estimates. Remaining challenges include the computational burden and the need to carefully manage prior-induced biases.

Paper II introduces an alternative to the method in Paper I. Instead of using an explicit prior, it exploits Deep Image Prior (DIP), which utilizes the structure of an untrained convolutional neural network to impose an implicit prior. This is implemented with Monte Carlo dropout, a simple approach to approximate Bayesian inference for uncertainty estimation. The method is easy to implement and denoises the tissue parameters T1, T2, and ADC. However, the results reveal that uncertainty calibration becomes more challenging, and the computation time remains too long for practical clinical use.

Paper III improves the DIP method from Paper II by addressing long computation times and difficulties in uncertainty calibration. To reduce computation times, we introduce warm-start initialization, which leverages information from both neighboring image slices and different subjects to accelerate parameter mapping. To improve calibration, we systematically tune MC dropout to reduce miscalibration. In addition, a data-driven early stopping criterion is proposed to automatically set the denoising level, removing the need for manual tuning. Together, these changes make the DIP method faster, better calibrated, and more clinically usable.

Paper IV investigates further improvements of the DIP method towards more advanced qMRI models, specifically evaluated with Patlak-based estimation of pharmacokinetic parameters in DCE-MRI. This study evaluates the feasibility of this approach by comparing parameter maps with and without the DIP method applied. Preliminary results show substantial noise reduction and improved feature representation. Remaining challenges include prior-induced biases that require further refinement.

In summary, this thesis addresses uncertainty in qMRI by focusing on two key components: reducing uncertainty through denoising and estimating the remaining uncertainty. These aspects are investigated using two fundamentally different strategies: one based on explicit denoising with robust Bayesian inference using MCMC (Paper I), and one based on implicit denoising combined with approximate Bayesian inference (Papers II-IV). The four included studies develop and refine these strategies to overcome practical limitations and enhance applicability. By evaluating their respective strengths and weaknesses, the work provides insight into how methodological choices affect accuracy, uncertainty, and computational feasibility. These contributions aim to support the development of qMRI as a more trustworthy and reproducible tool in cancer imaging and beyond.