System Matrix Recovery based on Adaptive Sparse Domain Selection in Magnetic Particle Imaging

System matrix (SM) acquisition is an important research content in magnetic particle imaging (MPI). In order to avoid a redundant and time-consuming calibration process, sparse representation of SM has been successfully used for SM recovery based on compressed sensing (CS) framework in the past decade. The success of sparse representation owes to the fact that SM is intrinsically sparse in some domain, such as DCT, DFT and wavelet. However, these sparse domains lack the adaptivity to local structures. Many dictionary learning methods aim at learning a universal and over-complete dictionary to represent various image structures, which gives us great inspiration. In SM recovery based on the CS framework, each row of SM can also be regarded as an image. Considering that the contents can vary significantly across different patches in each image, we propose to learn a set of compact sub-dictionaries from high quality SM image patches. The known SM image patches can be grouped into many clusters. A compact sub-dictionary can be learned for each cluster due to the similar patterns of each cluster. Since the adaptive selection of sub-dictionaries can better represent a given patch, the entire image can be recovered more accurately than using a universal dictionary. Then, by solving the inverse problem based on sparse regularization method, the recovered high-quality SM can be obtained. It is expected that this study will increase the practicability of MPI in biomedical applications and promote the development of MPI in the future