Sample Efficient Fourier Ptychography for Structured Data

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.