Flexible Array Shape Estimation Using Differentiable Beamforming

Promising advances in flexible array technology present new opportunities for wearable ultrasound. However, flexible arrays have non-rigid array shapes and thus unknown element positions, posing a major challenge for image reconstruction. We introduce a robust new method for estimating the shape of a flexible ultrasound array from the data itself. By implementing the delay-and-sum (DAS) beamformer in an automatic differentiation framework, we show that the phase error between translating subapertures can be used as a loss function that is backpropagated through DAS, all the way back to the element shape itself, allowing updates via gradient descent. We compare several loss functions, finding that the recently-introduced phase error loss has the best performance across a wide variety of speckle and point target phantom simulations.