Recently, many pulse-echo ultrasound (US) imaging methods have relied on the transmission of unfocused wavefronts. Such a strategy allows for very high frame rates at the cost of a degraded image quality. In this work, we present a regularized inverse problem approach and a highly efficient modeling of the physical measurement process to reconstruct high-quality US images from unfocused wavefronts. We compare it against a deep neural network (DNN) approach on the plane wave imaging challenge in medical ultrasound (PICMUS) and show that the use of carefully designed and trained DNN can overcome the limitations of standard image processing priors, which fail at capturing the very specific nature of US images accurately.