Dynamic cardiac MRI reconstruction using motion aligned locally low rank tensor (MALLRT)

Various sparse transform models have been explored for compressed sensing-based dynamic cardiac MRI reconstruction from vastly under-sampled k-space data. Recently emerged low rank tensor model using Tucker decomposition could be viewed as a special form of sparse model, where the core tensor, which is obtained using high-order singular value decomposition, is sparse in the sense that only a few elements have dominantly large magnitude. However, local details tend to be over-smoothed when the entire image is conventionally modeled as a global tensor. Moreover, low rankness is sensitive to motion as spatiotemporal correlation is corrupted by spatial misalignment between temporal frames. To overcome these limitations, this paper presents a novel motion aligned locally low rank tensor (MALLRT) model for dynamic MRI reconstruction. In MALLRT, low rank constraint is enforced on image patch-based local tensors, which correspond to overlapping blocks extracted from the reconstructed high-dimensional image after group-wise inter-frame motion registration. For solving the proposed model, this paper presents an efficient optimization algorithm by using variable splitting and alternating direction method of multipliers (ADMM). MALLRT demonstrated promising performance as validated on one cardiac perfusion MRI dataset and two cardiac tine MRI datasets using retrospective under-sampling with various acceleration factors, as well as one prospectively under-sampled cardiac perfusion MRI dataset. Compared to four state-of-the-art methods, MALLRT achieved substantially better image reconstruction quality in terms of both signal to error ratio (SER) and structural similarity index (SSIM) metrics, and visual perception in preserving spatial details and capturing temporal variations.