Fourier ptychography (FP) involves the acquisition of several low-resolution intensity images of a sample under several illumination angles. These images are then combined into a high-resolution complex-valued image given by the solution to a phase-retrieval problem. Dynamic FP, now, visualizes motion by considering a sequence of such high-resolution images. In this case, the large number of measurements required by standard frame-by-frame reconstruction methods does severely limit the temporal resolution, a drawback that we thwart in this work by proposing a neural-network-based reconstruction framework for dynamic FP. Specifically, we parameterize each image in the desired sequence as the output of a common untrained deep convolutional network driven by series of fixed input vectors that lie on a given one-dimensional (temporal) manifold. We then optimize the parameters of the network to globally fit the acquired measurements with proper time-stamping. The architecture of the network and the constraints on the input vectors impose a spatio-temporal regularization (deep spatio-temporal prior) on the sequence of images. We present numerical experiments that illustrate the ability of our new reconstruction method to achieve a much higher temporal resolution without compromising the spatial resolution.
Joint work with Pakshal Bohra, Thanh-an Pham, Yuxuan Long, Jaejun Yoo
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