Dynamic magnetic resonance imaging using compressed sensing with multi-scale low rank penalty

In multi-scale low rank decomposition model, the data are assumed to be a sum of block-wise low rank matrices with different scales of block sizes. In many practical applications, data itself is not represented directly, yet in some transformation domain, e.g. the data acquired in the Fourier domain in context of magnetic resonance imaging (MRI). In this paper, we present a natural extension of the multi-scale low rank model and propose its combination with a measurement operator. This modification is necessary for utilization of the model in compressed sensing perfusion MRI, where the compressed acquisition is crucial to achieve high spatial and temporal resolutions. We compare the proposed method with the recent “low-rank+ sparse” method of Otazo, Candes & Sodickson and we show that the proposed method brings improvement in the quality of reconstructed intensity curves.