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Quantitative Magnetic Resonance Imaging (qMRI) enables the reproduciblemeasurement of biophysical parameters in tissue. The challenge lies in solvinga nonlinear, ill-posed inverse problem to obtain the desired tissue parametermaps from acquired raw data. While various learned and non-learned approacheshave been proposed, the existing learned methods fail to fully exploit theprior knowledge about the underlying MR physics, i.e. the signal model and theacquisition model. In this paper, we propose PINQI, a novel qMRI reconstructionmethod that integrates the knowledge about the signal, acquisition model, andlearned regularization into a single end-to-end trainable neural network. Ourapproach is based on unrolled alternating optimization, utilizingdifferentiable optimization blocks to solve inner linear and non-linearoptimization tasks, as well as convolutional layers for regularization of theintermediate qualitative images and parameter maps. This design enables PINQIto leverage the advantages of both the signal model and learned regularization.We evaluate the performance of our proposed network by comparing it withrecently published approaches in the context of highly undersampled$T_1$-mapping, using both a simulated brain dataset, as well as real scannerdata acquired from a physical phantom and in-vivo data from healthy volunteers.The results demonstrate the superiority of our proposed solution over existingmethods and highlight the effectiveness of our method in real-world scenarios.

PINQI: An End-to-End Physics-Informed Approach to Learned Quantitative MRI Reconstruction