CCP SyneRBI
Collaborative Computational Project in Synergistic Reconstruction for Biomedical Imaging
Collaborative Computational Project in Synergistic Reconstruction for Biomedical Imaging
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Christina Brandt  Spatiotemporal 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 nonlinear 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 timelapse 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 spatiotemporal 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 invitro angioplasty. 

Kostas Papafitsoros  Quantitative MRI: From fingerprinting to integrated physicsbased 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):187193], magnetic resonance fingerprinting (MRF) was introduced as a technique being capable of simultaneously recovering such quantitative parameters by using a twostep 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 MRFtype algorithms is limited by the 'discretization size' of the dictionary, a novel physicsbased method for qMRI is proposed. In contrast to the conventional twostep method, our model is dictionaryfree and is rather governed by a single nonlinear equation, which is studied analytically. This nonlinear equation is efficiently solved via robustified Newtontype 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 modelbased reconstruction methods for MRI  Magnetic resonance imaging (MRI) is based on serial scanning of Fourier (kspace) 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 nonlinearly on parameters that characterize tissuespecific 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 welldefined 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 pixelwise fitted to a physicbased signal model to obtain the quantitative parameter maps. As this requires the acquisition of several fullysampled images with different contrast, this is very time consuming and inefficient. Novel iterative methods can estimate the parameters directly from the kspace data by solving a nonlinear 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 nonsmooth 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 nonsmooth (i.e. nondifferentiable) optimization problems. For instance directional total variation can be used to incorporate anatomical information from MRI into the PET reconstruction. However, since nonsmooth 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 nonsmooth 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. 
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