An apparatus was developed for obtaining emission transaxial images of sections of organs containing positron-emitting radiopharmaceuticals. The detection system is a hexagonal array of 24 NaI(T1) detectors connected to coincidence circuits to achieve the "electronic" collimation of annihilation photons. The image is formed by a computer-applied algorithm which provides quantitative reconstruction of the distribution of activity. Computer simulations, phantom and animal studies show that this approach is capable of providing images of better contrast and resolution than are obtained with scintillation cameras. Advantages of positron vs. single photon reconstruction tomography are discussed.