Acceleration of Perfusion MRI Using Locally Low-Rank Plus Sparse Model Marie Daˇ nkov´ a 1, 2 , Pavel Rajmic 1 , and Radovan Jiˇ r´ ık 3 1 SPLab, Brno University of Technology, Brno, Czech Republic m.dankova@phd.feec.vutbr.cz, rajmic@feec.vutbr.cz 2 CEITEC, Masaryk University, Brno, Czech Republic 3 ASCR, Institute of Scientific Instruments, Brno, Czech Republic jirik@isibrno.cz Abstract. Perfusion magnetic resonance imaging is a technique used in diagnostics and evaluation of therapy response, where the quantification is done by analyzing the perfusion curves. Perfusion- and permeability- related tissue parameters can be obtained using advanced pharmacoki- netic models, but, these models require high spatial and temporal res- olution of the acquisition simultaneously. The resolution is usually in- creased by means of compressed sensing: the acquisition is accelerated by under-sampling. However, these techniques need to be improved to achieve higher spatial resolution and/or to allow multislice acquisition. We propose a modification of the L+S model for the reconstruction of perfusion curves from the under-sampled data. This model assumes that perfusion data can be modelled as a superposition of locally low-rank data and data that are sparse in the spectral domain. We show that our model leads to a better performance compared to the other methods. Keywords: perfusion, MRI, DCE-MRI, compressed sensing, sparsity, locally low-rank 1 Introduction Perfusion magnetic resonance imaging (MRI), more specifically the dynamic contrast enhanced MRI (DCE-MRI) [1–4], is nowadays a promising method for medical diagnosis and evaluation of therapy response. Using perfusion MRI, on- cological and cardiovascular diseases can be diagnosed and their effective treat- ment can be monitored. In perfusion MRI, a suitable contrast agent is admin- istered intravenously. Due to the cardiovascular system, the contrast agent is distributed within the organism and its temporal and spatial distribution can be observed and analyzed. The time dependency of contrast agent concentration in a region of interest is called perfusion curve(s). The tissue-specific perfusion parameters, necessary for the diagnosis, are estimated from the perfusion curves by approximation using a pharmacokinetic model. The usual pharmacokinetic models in use are the Tofts and the extended Tofts models [5], which only allow estimating of a limited number of perfusion