Conflict-cost based random sampling design for parallel MRI with low rank constraints

In compressed sensing MRI, it is very important to design sampling pattern for random sampling. For example, SAKE (simultaneous auto-calibrating and k-space estimation) is a parallel MRI reconstruction method using random undersampling. It formulates image reconstruction as a structured low-rank matrix completion problem. Variable density (VD) Poisson discs are typically adopted for 2D random sampling. The basic concept of Poisson disc generation is to guarantee samples are neither too close to nor too far away from each other. However, it is difficult to meet such a condition especially in the high density region. Therefore the sampling becomes inefficient. In this paper, we present an improved random sampling pattern for SAKE reconstruction. The pattern is generated based on a conflict cost with a probability model. The conflict cost measures how many dense samples already assigned are around a target location, while the probability model adopts the generalized Gaussian distribution which includes uniform and Gaussian-like distributions as special cases. Our method preferentially assigns a sample to a k-space location with the least conflict cost on the circle of the highest probability. To evaluate the effectiveness of the proposed random pattern, we compare the performance of SAKEs using both VD Poisson discs and the proposed pattern. Experimental results for brain data show that the proposed pattern yields lower normalized mean square error (NMSE) than VD Poisson discs.