Related papers: A variational approach to the inverse photolithogr…
The polarisation of light is a powerful and widely used degree of freedom to encode information, both in classical and quantum applications. In particular, quantum information technologies based on photons are being revolutionised by the…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
Optical multilayer thin film structures have been widely used in numerous photonic domains and applications. The key component to enable these applications is the inverse design. Different from other photonic structures such as metasurface…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…
This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…
A polarization camera has great potential for 3D reconstruction since the angle of polarization (AoP) of reflected light is related to an object's surface normal. In this paper, we propose a novel 3D reconstruction method called…
The inverse problem of X-tray transforms considers reconstructing functions from some data that are easier to measure, which is typically the integral of that function along geodesics. We prove that if the domain has a foliation structure,…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction…
Estimating shape and appearance of a three dimensional object from a given set of images is a classic research topic that is still actively pursued. Among the various techniques available, PS is distinguished by the assumption that the…
Superposing multiple plane waves can generate helicity lattices in which the optical helicity varies regularly in space. Here we propose an inverse design method for constructing arbitrary helicity structures based on placing a digital…
We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling, which essentially seeks to…
Image anomaly detection consists in detecting images or image portions that are visually different from the majority of the samples in a dataset. The task is of practical importance for various real-life applications like biomedical image…
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…
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…
Although the vectorization operation is known and well-defined, it is only defined for 2-D matrices, and its inverse isn't as well-popularized. This work proposes to generalize the vectorization to higher dimensions, and define…