Related papers: A generalization bound for exit wave reconstructio…
Lorentz transmission electron microscopy is a unique characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials at high spatial resolution. The quantitative information…
Deep learning provides a new avenue for image restoration, which demands a delicate balance between fine-grained details and high-level contextualized information during recovering the latent clear image. In practice, however, existing…
We investigate the amount of primordial information that can be reconstructed from spectroscopic galaxy surveys, as well as what sets the noise in reconstruction at low wavenumbers, by studying a simplified universe in which galaxies are…
In this paper we consider the mathematical model of thermo- and photo-acoustic tomography for the recovery of the initial condition of a wave field from knowledge of its boundary values. Unlike the free-space setting, we consider the wave…
This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…
Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET…
Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some…
For nonconvex and nonsmooth restoration models, the lower bound theory reveals their good edge recovery ability, and related analysis can help to design convergent algorithms. Existing such discussions are focused on isotropic…
In this paper, we consider the highly ill-posed problem of jointly recovering two real-valued signals from the phaseless measurements of their circular convolution. The problem arises in various imaging modalities such as Fourier…
This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…
As a burgeoning technique, out-of-focus electron ptychography offers the potential for rapidly imaging atomic-scale large fields of view (FoV) using a single diffraction dataset. However, achieving robust out-of-focus ptychographic…
Reconstructing accurate surfaces from sparse multi-view images remains challenging due to severe geometric ambiguity and occlusions. Existing generalizable neural surface reconstruction methods primarily rely on cost volumes that summarize…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
Parameter estimation of gravitational wave data is often computationally expensive, requiring simplifying assumptions such as circularisation of binary orbits. Although, if included, the sub-dominant effects like orbital eccentricity may…
In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set…
This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known…
Enforcing alignment between the internal representations of diffusion or flow-based generative models and those of pretrained self-supervised encoders has recently been shown to provide a powerful inductive bias, improving both convergence…
Metasurfaces are subwavelength-structured artificial media that can shape and localize electromagnetic waves in unique ways. The inverse design of these devices is a non-convex optimization problem in a high dimensional space, making global…
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…