# CCP PET-MR

*Collaborative Computational Project in Positron Emission Tomography
and Magnetic Resonance imaging*

*Collaborative Computational Project in Positron Emission Tomography
and Magnetic Resonance imaging*

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Christina Brandt | Spatio-temporal regularization for 4D magnetic particle imaging | Magnetic particle imaging (MPI) is a new imaging modality which can capture fast dynamic processes in 3D volumes, based on the non-linear response of the magnetic particles to an applied magnetic field. Possible medical applications are vascular imaging, device tracking, stem cell imaging and magnetic hyperthermia. However, even in the case of time-lapse data, the standard reconstruction approach consists in static regularization methods such as classical Tikhonov regularization applied to each single time frame. In this talk, we propose to make use of the high temporal regularity of the data and formulate a quadratic spatio-temporal regularization which can be efficiently solved using a low rank approximation of the forward operator. We illustrate our reconstruction approach with real dynamic data of a prototypical application which is the tracking of a catheter during a in-vitro angioplasty. |

Kostas Papafitsoros | Quantitative MRI: From fingerprinting to integrated physics-based models | Quantitative magnetic resonance imaging (qMRI) is concerned with estimating (in physical units) values of magnetic and tissue parameters, e.g., relaxation times T1, T2, or proton density. Recently, in [Ma et al, Nature, 495 (2013):187-193], magnetic resonance fingerprinting (MRF) was introduced as a technique being capable of simultaneously recovering such quantitative parameters by using a two-step procedure: (i) given a probe, a series of magnetization maps are computed and then (ii) matched to (quantitative) parameters with the help of a precomputed dictionary which is related to the Bloch manifold. In this talk, we first put MRF and its variants into perspective with optimization and inverse problems to gain mathematical insights concerning identifiability of parameters under noise and interpretation in terms of optimizers. Motivated by the fact that the Bloch manifold is nonconvex and that the accuracy of the MRF-type algorithms is limited by the 'discretization size' of the dictionary, a novel physics-based method for qMRI is proposed. In contrast to the conventional two-step method, our model is dictionary-free and is rather governed by a single nonlinear equation, which is studied analytically. This nonlinear equation is efficiently solved via robustified Newton-type methods. The effectiveness of the new method for noisy and undersampled data is shown both analytically and via extensive numerical examples, for which improvement over MRF and its variants is also documented. |

Martin Uecker | Nonlinear model-based reconstruction methods for MRI | Magnetic resonance imaging (MRI) is based on serial scanning of Fourier (k-space) data of a magnetization image in a repeated series of magnetic resonance experiments. To obtain consistent data for reconstruction of an individual image, exactly he same state of the magnetization has to be prepared in each repetition. These images then depend non-linearly on parameters that characterize tissue-specific chemical environment of the nuclear spins or physical processes such as flow, diffusion, perfusion, or temperature. The qualitative nature of conventional MR images makes quantitative analysis difficult as the image contrast depends on the specific measurement technique and equipment. In contrast, in quantitative MRI the underlying physical parameters are estimated. Results can then quantitatively be compared across sites and retrospectively processed to synthetically create MR images with well-defined and reproducible contrast. Currently, quantitative MRI is based on the acquisition of many images with different measurement protocols (e.g. echo times, flip angle, etc.), which are then pixel-wise fitted to a physic-based signal model to obtain the quantitative parameter maps. As this requires the acquisition of several fully-sampled images with different contrast, this is very time consuming and inefficient. Novel iterative methods can estimate the parameters directly from the k-space data by solving a non-linear inverse problem - completely avoiding the reconstruction of intermediate images and opening the way for highly efficient quantitative MRI. These new techniques can be understood as synergistic reconstruction of multiple MRI images with different contrast that exploits known correlations. In this talk, we will discuss the underlying ideas as well as recent developments. |

Matthias Ehrhardt | Fast preconditioned reconstruction with non-smooth anatomical priors by randomisation |
Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins). The last decades have seen tremendous advancements in mathematical imaging tools many of which lead to non-smooth (i.e. non-differentiable) optimization problems. For instance directional total variation can be used to incorporate anatomical information from MRI into the PET reconstruction. However, since non-smooth optimization problems are hard to solve, most of these tools have not been translated to clinical PET data. In this work, inspired by big data machine learning applications, we use advanced randomized optimization algorithms to solve the PET reconstruction problem for a very large class of non-smooth priors which includes for example directional total variation. The proposed algorithm randomly uses subsets of the data and only updates the variables associated with these. While this idea often leads to divergent algorithms, we show that the proposed algorithm does indeed converge for any proper subset selection. Numerically, we show on real PET data (FDG and florbetapir) from a Siemens Biograph mMR that about ten projections and backprojections are sufficient to solve the optimisation problem. |