A Radon diffraction theorem for plane wave ultrasound imaging

The rising demand on high frame rate ultrasound imaging applications necessitates the development of fast algorithms for plane wave image reconstruction. We introduce a new class of plane wave reconstructions that relies on a relation between receive data and image data in the Radon domain. This relation is derived for arbitrary dimensions and validated on multiple two-dimensional plane wave data sets. We further present a mathematical relation between conventional delay-and-sum and Fourier domain reconstruction methods and the method proposed. Our analysis shows that they all rely on the same physical model with slight variations in certain filtering steps and, therefore, the new Radon domain reconstruction yields similar results as other methods in terms of image quality. However, we show that our method offers a huge potential to improve computation time by reducing the number of applied projections and to improve image quality by introducing nonlinear operations in the Radon domain, e.g., for edge enhancement. As the Radon transform retains both angular and temporal information, the relation also provides new insights on the fundamentals of plane wave imaging that can be leveraged for optimizing acquisition schemes or for developing novel compounding strategies in the future.