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The design and evaluation of the imaging system Clear-PEM for positron emission mammography, under development by the PEM Consortium within the framework of the Crystal Clear Collaboration at CERN, is presented. The proposed apparatus is based on fast, segmented, high atomic number radiation sensors with depth-of-interaction measurement capabilities, and state-of-the-art data acquisition techniques. The camera consists of two compact and planar detector heads with dimensions 16.5×14.5 cm2 for breast and axilla imaging. Low-noise integrated electronics provide signal amplification and analog multiplexing based on a new data-driven architecture. The coincidence trigger and data acquisition architecture makes extensive use of pipeline processing structures and multi-event memories for high efficiency up to a data acquisition rate of one million events/s. Experimental validation of the detection techniques, namely the basic properties of the radiation sensors and the ability to measure the depth-of-interaction of the incoming photons, are presented. System performance in terms of detection sensitivity, count-rates and reconstructed image spatial resolution were also evaluated by means of a detailed Monte Carlo simulation and an iterative image reconstruction algorithm.