Non-destructive characterization of multi-layered structures that can be accessed from only a single side is important for applications such as well-bore integrity inspection. Existing methods related to Synthetic Aperture Focusing Technique (SAFT) rapidly produce acceptable results but with significant artifacts. Recently, ultrasound model-based iterative reconstruction (UMBIR) approaches have shown significant improvements over SAFT. However, even these methods produce ringing artifacts due to the high fractional-bandwidth of the excitation signal. In this paper, we propose a ringing artifact reduction method for ultrasound image reconstruction that uses a multi-agent consensus equilibrium (RARE-MACE) framework. Our approach integrates a physics-based forward model that accounts for the propagation of a collimated ultrasonic beam in multi-layered media, a spatially varying image prior, and a denoiser designed to suppress the ringing artifacts that are characteristic of reconstructions from high-fractional bandwidth ultrasound sensor data. We test our method on simulated and experimental measurements and show substantial improvements in image quality compared to SAFT and UMBIR.