Positron emission tomography (PET) images are widely used in many clinical applications, such as tumor detection and brain disorder diagnosis. To obtain PET images of diagnostic quality, a sufficient amount of radioactive tracer has to be injected into a living body, which will inevitably increase the risk of radiation exposure. On the other hand, if the tracer dose is considerably reduced, the quality of the resulting images would be significantly degraded. It is of great interest to estimate a standard-dose PET (S-PET) image from a low-dose one in order to reduce the risk of radiation exposure and preserve image quality. This may be achieved through mapping both S-PET and low-dose PET data into a common space and then performing patch-based sparse representation. However, a one-size-fits-all common space built from all training patches is unlikely to be optimal for each target S-PET patch, which limits the estimation accuracy. In this paper, we propose a data-driven multi-level canonical correlation analysis scheme to solve this problem. In particular, a subset of training data that is most useful in estimating a target S-PET patch is identified in each level, and then used in the next level to update common space and improve estimation. In addition, we also use multi-modal magnetic resonance images to help improve the estimation with complementary information. Validations on phantom and real human brain data sets show that our method effectively estimates S-PET images and well preserves critical clinical quantification measures, such as standard uptake value.