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In this paper, the preliminary design and assessment of a high-resolution 3-D acoustic imaging system based on a sparse planar array of sensors, which is particularly intended for underwater applications, are presented. Critical issues in the development of high-resolution 3-D sonar systems are 1) the cost of hardware, which is associated with the huge number of sensors that compose the planar array, and 2) the computational burden of processing the signals that were gathered. Here, such problems are overcome by the optimized synthesis of an aperiodic sparse array that allows the device to operate at different frequencies, yielding an acceptable sidelobe level and a good tradeoff between the field of view and the resolution. The array optimization is performed using an efficient stochastic method, in which the number of sensors is minimized, whereas their positions and weights are simultaneously optimized. To test the validity of the designed system, the signals that the sparse array received in response to the insonification of a scene with a wideband pulse are simulated, and voxel-based beamforming is applied to generate the 3-D image. The obtained images show high fidelity to the geometrical characteristics of the scene, in accordance with the expected performance of the 3-D sonar system.