Multi-objective optimization of virtual source distributions for ultrafast diverging wave imaging

Diverging wave imaging (DWI) with coherent compounding addresses the field-of-view (FOV) limitations of ultrafast imaging by placing virtual sources (VSs) behind the transducer. The number and spatial distribution of these VSs affects both image quality and frame rate, making them of high interest. Existing approaches use deterministic placements (e.g., linear, tilted, and Archimedean-spiral distributions), which exhibit inherent trade-offs between resolution and contrast. However, the optimal placement of VSs to maximize image quality has not yet been investigated for convex arrays. In this study, we propose a multi-objective genetic algorithm to optimize VS spatial distributions with a compound mask weighting strategy - mapped from transmit apodization in synthetic aperture imaging (SAI) - to enhance beam coherence and reduce artifacts during optimization. The framework was evaluated across different numbers of VSs to quantify performance trade-offs under fewer transmission events. The proposed multi-objective framework optimizes two PSF-based metrics, namely the Full Width at Half Maximum (FWHM) and the Peak Sidelobe Level (PSL). Then, image-quality metrics, such as contrast ratio (CR) and signal-to-noise ratio (SNR), are computed a posteriori as independent validation measures on the reconstructed images. In both simulations and experimental trials, the optimized VS distributions achieved up to a 50% reduction in FWHM and a 60% improvement in CR compared to deterministic methods, while preserving these gains even with reduced transmission events.