Consensus equilibrium-based ultrasound imaging with joint multi-frequency modeling

Ultrasound imaging is widely used in non-destructive testing (NDT), but conventional reconstruction methods such as the Synthetic Aperture Focusing Technique (SAFT) often suffer from artefacts and limited resolution. Model-based approaches such as UMBIR improve image quality but require large-scale optimisation in order to process multiple frequencies jointly. This paper introduces a Multi-Frequency Multi-Agent Consensus Equilibrium (MMACE) framework that integrates measurements from multiple excitation frequencies within a unified consensus optimisation. The method employs forward model agents for frequency-specific data consistency and prior agents including qGGMRF and ringing-aware BM3D regularisation. Results show that MMACE achieves on average a 2.3 dB improvement in PSNR, a 12% increase in SSIM, and a 15% higher recall of defect boundaries compared to UMBIR and multi-frequency UMBIR. These results demonstrate that MMACE offers robust suppression of ringing artefacts and improved localisation of structural features, establishing a new benchmark for ultrasound NDT imaging.