Underwater acoustic imaging employs a special form of array which includes numerous transducer elements to achieve beamforming. Although a large-scale array can bring high imaging resolution, it will also cause difficulties in hardware complexity and real-time application. In this paper, in order to reduce the number of array elements, a sparse optimization for Mills cross is proposed, considering the elements’ distributions and weights design. The improved genetic algorithm is adopted to generate evolutions for sparse solution. In order to ensure effective convergence and successful evolution, relevant genetic operators are proposed, including appropriate population coding, correct fitness function, reasonable selection strategy and efficient two-point orthogonal crossover, among others. Essentially, a satisfied sparse solution is a result of mutual restraint between array elements’ survivals and their weights. The simulations reveal that our sparse cross array decreases the number of elements by 8.25% compared to the conventional Mills cross multiplicative array, while keeping the advantages of narrow main lobe width and low sidelobe level. Improved genetic algorithm is an effective method for the underwater acoustic imaging array to implement the sparse optimization.

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