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Lensless imaging is a new, emerging modality where image sensors utilize optical elements in front of the sensor to perform multiplexed imaging. There have been several recent papers to reconstruct images from lensless imagers, including methods that utilize deep learning for state-of-the-art performance. However, many of these methods require explicit knowledge of the optical element, such as the point spread function, or learn the reconstruction mapping for a single fixed PSF. In this paper, we explore a neural network architecture that performs joint image reconstruction and PSF estimation to robustly recover images captured with multiple PSFs from different cameras. Using adversarial learning, this approach achieves improved reconstruction results that do not require explicit knowledge of the PSF at test-time and shows an added improvement in the reconstruction model's ability to generalize to variations in the camera's PSF. This allows lensless cameras to be utilized in a wider range of applications that require multiple cameras without the need to explicitly train a separate model for each new camera.