Fig. 2. Learning pipelines for BPF and image reconstruction network.

To begin, the phase filter is initialized with a continuous axi-symmetric function (e.g., axicon) and penalized by a nonlinear function that is designed to enforce the phase value in each ring to the binary states through the training process. The imaging model then predicts the image, which is then fed into the U-Net-based image reconstruction network to obtain the network output. This network output is compared against the ground-truth image, and optimization is performed to minimize the difference through a gradient-descent method