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Ptychography is a well-established coherent diffraction imaging technique that enables non-invasive imaging of samples at a nanometer scale. It has been extensively used in various areas such as the defense industry or materials science.…

Ptychography is a well-studied phase imaging method that makes non-invasive imaging possible at a nanometer scale. It has developed into a mainstream technique with various applications across a range of areas such as material science or…

Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such…

X-ray computed tomography (CT) reconstructs the internal morphology of a three dimensional object from a collection of projection images, most commonly using a single rotation axis. However, for objects containing dense materials like…

The quantum analogue of ptychography, a powerful coherent diffractive imaging technique, is a simple method for reconstructing $d$-dimensional pure states. It relies on measuring partially overlapping parts of the input state in a single…

Ptychography is now integrated as a tool in mainstream microscopy allowing quantitative and high-resolution imaging capabilities over a wide field of view. However, its ultimate performance is inevitably limited by the available coherent…

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging technique that holds great promise for biomedical imaging. PACT is a hybrid imaging method that can exploit the strong endogenous…

Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A…

Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…

Ptychography promises diffraction limited resolution without the need for high resolution lenses. To achieve high resolution one has to solve the phase problem for many partially overlapping frames. Here we review some of the existing…

X-ray ptychography is a cutting edge imaging technique providing ultra-high spatial resolutions. In ptychography, phase retrieval, i.e., the recovery of a complex valued signal from intensity-only measurements, is enabled by exploiting a…

Multislice electron ptychography (MEP) is an inverse imaging technique that computationally reconstructs the highest-resolution images of atomic crystal structures from diffraction patterns. Available algorithms often solve this inverse…

Advances in bioimaging methods and hardware facilities have revolutionised the determination of numerous biological structures at atomic or near-atomic resolution. Among these developments, electron ptychography has recently attracted…

Ptychography is an imaging technique that captures multiple overlapping snapshots of a sample, illuminated coherently by a moving localized probe. The image recovery from ptychographic data is generally achieved via an iterative algorithm…

We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…

While the advances in synchrotron light sources, together with the development of focusing optics and detectors, allow nanoscale ptychographic imaging of materials and biological specimens, the corresponding experiments can yield…

X-ray computed tomography (CT) based on photon counting detectors (PCD) extends standard CT by counting detected photons in multiple energy bins. PCD data can be used to increase the contrast-to-noise ratio (CNR), increase spatial…

One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only…

Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…

We consider the problem of blind ptychography, that is the joint estimation of an unknown object and an illumination function from diffraction intensity measurements. In ptychography, diffraction measurements from neighboring regions of the…