Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is sufficient to capture a great deal of low-level image statistics prior to any learning. In order to do so, we show that a randomly-initialized neural network can be used as a handcrafted prior with excellent results in standard inverse problems such as denoising, super-resolution, and inpainting. Furthermore, the same prior can be used to invert deep neural representations to diagnose them, and to restore images based on flash-no flash input pairs. 
Apart from its diverse applications, our approach highlights the inductive bias captured by standard generator network architectures. It also bridges the gap between two very popular families of image restoration methods: learning-based methods using deep convolutional networks and learning-free methods based on handcrafted image priors such as self-similarity. Code and supplementary material are available at this https URL .

Deep Image Prior

Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either “zoom in” and image at high-resolution, or they can “zoom out” to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges.

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Fourier ptychography: current applications and future promises

Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is sufficient to capture a great deal of low-level image statistics prior to any learning. In order to do so, we show that a randomly-initialized neural network can be used as a handcrafted prior with excellent results in standard inverse problems such as denoising, super-resolution, and inpainting. Furthermore, the same prior can be used to invert deep neural representations to diagnose them, and to restore images based on flash-no flash input pairs. Apart from its diverse applications, our approach highlights the inductive bias captured by standard generator network architectures. It also bridges the gap between two very popular families of image restoration methods: learning-based methods using deep convolutional networks and learning-free methods based on handcrafted image priors such as self-similarity (Code and supplementary material are available at https://dmitryulyanov.github.io/deep_image_prior).

The competition between resolution and the imaging field of view is a long-standing problem in traditional imaging systems — they can produce either an image of a small area with fine details or an image of a large area with coarse details. Fourier ptychography (FP) is an approach for tackling this intrinsic trade-off in imaging systems. It takes the challenge of high-throughput and high-resolution imaging from the domain of improving the physical limitations of optics to the domain of computation. It also enables post-measurement computational correction of optical aberrations. We present the basic concept of FP, compare it to related imaging modalities and then discuss experimental implementations, such as aperture-scanning FP, macroscopic camera-scanning FP, reflection mode, single-shot set-up, X-ray FP, speckle-scanning scheme and deep-learning-related implementations. Various applications of FP are discussed, including quantitative phase imaging in 2D and 3D, digital pathology, high-throughput cytometry, aberration metrology, long-range imaging and coherent X-ray nanoscopy. A collection of datasets and reconstruction codes is provided for readers interested in implementing FP themselves. Fourier ptychography is an imaging approach that addresses the intrinsic trade-off between resolution and field of view in optical systems and provides computational correction of optical aberrations. This Technical Review surveys its implementations and applications.

Concept, implementations and applications of Fourier ptychography

Low signal-to-noise ratio (SNR) measurements, primarily due to the quartic attenuation of intensity with distance, are arguably the fundamental barrier to real-time, high-resolution, non-line-of-sight (NLoS) imaging at long standoffs. To better model, characterize, and exploit these low SNR measurements, we use spectral estimation theory to derive a noise model for NLoS correlography. We use this model to develop a speckle correlation-based technique for recovering occluded objects from indirect reflections. Then, using only synthetic data sampled from the proposed noise model, and without knowledge of the experimental scenes nor their geometry, we train a deep convolutional neural network to solve the noisy phase retrieval problem associated with correlography. We validate that the resulting deep-inverse correlography approach is exceptionally robust to noise, far exceeding the capabilities of existing NLoS systems both in terms of spatial resolution achieved and in terms of total capture time. We use the proposed technique to demonstrate NLoS imaging with 300 µm resolution at a 1 m standoff, using just two 1/8th ${s}$s exposure-length images from a standard complementary metal oxide semiconductor detector.

Deep-inverse correlography: towards real-time high-resolution non-line-of-sight imaging

Fourier Ptychography is a recently proposed imaging technique that yields high-resolution images by computationally transcending the diffraction blur of an optical system. At the crux of this method is the phase retrieval algorithm, which is used for computationally stitching together low-resolution images taken under varying illumination angles of a coherent light source. However, the traditional iterative phase retrieval technique relies heavily on the initialization and also need a good amount of overlap in the Fourier domain for the successively captured low-resolution images, thus increasing the acquisition time and data. We show that an auto-encoder based architecture can be adaptively trained for phase retrieval under both low overlap, where traditional techniques completely fail, and at higher levels of overlap. For the low overlap case we show that a supervised deep learning technique using an autoencoder generator is a good choice for solving the Fourier ptychography problem. And for the high overlap case, we show that optimizing the generator for reducing the forward model error is an appropriate choice. Using simulations for the challenging case of uncorrelated phase and amplitude, we show that our method outperforms many of the previously proposed Fourier ptychography phase retrieval techniques.

Mayug Maniparambil

Papers

Phase retrieval for Fourier Ptychography under varying amount of measurements

Phase retrieval for Fourier Ptychography under varying amount of measurements.