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With 3D magnetic resonance imaging (MRI), a tradeoff exists between higher image quality and shorter scan time. One way to solve this problem is to reconstruct high-quality MRI images from undersampled k-space. There have been many recent studies exploring effective k-space undersampling patterns and designing MRI reconstruction methods from undersampled k-space, which are two necessary steps. Most studies separately considered these two steps, although in theory, their performance is dependent on each other. In this study, we propose a joint optimization model, trained end-to-end, to simultaneously optimize the undersampling pattern in the Fourier domain and the reconstruction model in the image domain. A 2D probabilistic undersampling layer was designed to optimize the undersampling pattern and probability distribution in a differentiable manner. A 2D inverse Fourier transform layer was …