Low-rank plus sparse decomposition based dynamic myocardial perfusion PET image restoration

Objectives To improve the absolute quantitation of dynamic myocardial perfusion (MP) PET imaging through low-rank plus sparse decomposition based MP PET image restoration.

Methods In conventional image restoration models, a single constraint is assumed to regularize the ill-posed problem. We propose that image restoration should be based on multiple constraints, given the fact that image characteristics are hardly captured with a single constraint. At the same time, it may be possible, but not optimal to regularize the image with multiple constraints simultaneously. Fortunately, MP PET images can be decomposed into a superposition of background vs. dynamic components via low rank plus sparse (namely L+S) decomposition. Thus, we proposed a low-rank plus sparse decomposition based MP PET image restoration model and expressed it as a convex optimization problem. An algorithm was developed to solve the convex optimization problem based on iterative soft thresholding method. Using realistic dynamic Rb-82 MP PET data, we optimized the performance of the proposed restoration model with L+S decomposition, and compared its performance with restoration model with sparse constraint only as well as simultaneous low-rank and sparse (L&S) constraints.

Results The proposed L+S decomposition based MP PET images restoration model resulted in substantial visual as well as quantitative accuracy improvements in terms of noise versus bias performance as demonstrated in extensive Rb-82 MP PET simulations. In particular, the proposed restoration model exhibited 50% and 25% noise reduction in noise level with matched bias compared to restoration model with sparse constraint only, as well as simultaneous L&S constraints.

Conclusions The proposed low-rank plus sparse (L+S) decomposition based MP PET images restoration model resulted in enhanced quantitative performance compared to restoration model with sparse constraint only, as well as simultaneous low-rank and sparse (L&S) constraints.

Research Support This work was supported by the 973 Program of China under grant no. 2010CB732503 and the Specialized Research Fund for the Doctoral Program of Higher Education under grant 20134433120017.