We study the problem of recovering structured data from Fourier ptychography measurements. Fourier ptychography is an image acquisition scheme that uses an array of images to produce high-resolution images in microscopy as well as long-distance imaging, to mitigate the effects of diffraction blurring. The number of measurements is typically much larger than the size of the signal (image or video) to be reconstructed, which translates to high storage and computational requirements. The issue of high sample complexity can be alleviated by utilizing structural properties of the image (or video). In this article, we first discuss a range of sub-sampling schemes which can reduce the amount of measurements in Fourier ptychography setups; however, this makes the problem ill-posed. Correspondingly, we impose structural constraints on the signals to be recovered, to regularize the problem. Through our novel framework of recovery algorithms, we show that one can reconstruct high-resolution images (or video) from fewer samples, via simple and natural assumptions on the structure of the images (or video). We demonstrate the validity of our claims through a series of experiments, both on simulated and real data.

中文翻译：

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结构化数据的样本高效傅立叶印刷术

我们研究从傅立叶 ptychography 测量中恢复结构化数据的问题。Fourier ptychography 是一种图像采集方案，它使用图像阵列在显微镜和长距离成像中产生高分辨率图像，以减轻衍射模糊的影响。测量次数通常远大于要重建的信号（图像或视频）的大小，这意味着高存储和计算要求。可以通过利用图像（或视频）的结构特性来缓解高样本复杂性的问题。在本文中，我们首先讨论了一系列子采样方案，这些方案可以减少傅立叶 ptychography 设置中的测量量；然而，这使得问题不合适。相应地，我们对要恢复的信号施加结构性约束，以规范问题。通过我们新颖的恢复算法框架，我们表明可以通过对图像（或视频）结构的简单自然假设，从更少的样本中重建高分辨率图像（或视频）。我们通过一系列实验证明了我们的主张的有效性，包括模拟数据和真实数据。