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A high-performance positron emission tomography (PET) scanner, which measures depth-of-interaction (DOI) information, is under development at the National Institute of Radiological Sciences in Japan. Image reconstruction methods with accurate modeling of the system response functions have been successfully used to improve PET image quality. It is, however, difficult to apply these methods to the DOI-PET scanner because the dimension of DOI-PET data increases in proportion to the square of the number of DOI layers. In this paper, we propose a compressed imaging system model for DOI-PET image reconstruction, in order to reduce computational cost while keeping image quality. The basic idea of the proposed method is that the DOI-PET imaging system is highly redundant. First, DOI-PET data is transformed into compact data so that data bins with highly correlating sensitivity functions are combined. Then image reconstruction methods based on accurate system modeling, such as the maximum likelihood expectation maximization (ML-EM), are applied. The proposed method was applied to simulated data for the DOI-PET scanner operated in 2-D mode. Then the tradeoff between the background noise and the spatial resolution was investigated. Numerical simulation results show that the proposed method followed by ML-EM reduces computational cost effectively while keeping the advantages of the accurate system modeling and DOI information.