Simultaneous PET image restoration and tumor segmentation using a generalized linear model: A global optimal solution

Objectives Partial volume effect (PVE) is a major reason degrading tumor segmentation accuracy in PET. We proposed a new global optimal segmentation method using a generalized linear model, which couples image restoration and segmentation.

Methods Image restoration and segmentation were achieved simultaneously by minimizing an energy functional. The energy functional consists of a new data-fitting term and a classical total variation (TV) regularization term. The data-fitting term was derived from a generalized linear model (GLM) formulation of image intensity and expressed as the integral over image domain of a Bregman divergence. We derived the shape gradient of this data-fitting term and studied the convex relaxation. A new alternating split-Bregman algorithm was introduced to solve the minimization problem and the globally optimal solution of the original non-convex problem was obtained. Segmentation performance of the proposed method was tested on twenty patients with esophageal cancer. For comparison, the widely used thresholding methods with 42% and 50% SUV_max as thresholds, Otsu, Fuzzy C-mean Clustering (FCM), Active Contours (AC), Geodesic Active Contours (GAC), and Graph Cuts (GC) method were also tested. Dice similarity index (DSI) and classification error (CE) were calculated to evaluate the segmentation accuracy.

Results The proposed method significantly outperformed all other tested methods. It has an average DSI and CE of 0.83 and 0.31, while the FCM method — the second best one — has only an average DSI and CE of 0.69 and 0.47.

Conclusions Coupling image restoration and segmentation can handle PVE and thus improves tumor segmentation accuracy in PET. The presented GLM model has globally optimal solution which is more robust than other tested segmentation methods.

Research Support Shan Tan was supported in part by National Natural Science Foundation of China (NNSFC), under Grant Nos. 60971112 and 61375018, and Fundamental Research Funds for the Central Universities, under Grant No. 2012QN086. Wei Lu was supported in part by the National Institutes of Health (NIH) Grant No. R01 CA172638.