Related papers: Robustness of data-driven approaches in limited an…
We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value decomposition-based…
Computer vision tasks require processing large amounts of data to perform image classification, segmentation, and feature extraction. Optical preprocessors can potentially reduce the number of floating point operations required by computer…
In transmission X-ray microscopy (TXM) systems, the rotation of a scanned sample might be restricted to a limited angular range to avoid collision to other system parts or high attenuation at certain tilting angles. Image reconstruction…
While filtered back projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a…
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…
Radon transform is widely used in physical and life sciences and one of its major applications is the X-ray computed tomography (X-ray CT), which is significant in modern health examination. The Radon inversion or image reconstruction is…
Recently, experiments have been reported where researchers were able to perform high dynamic range (HDR) tomography in a heuristic fashion, by fusing multiple tomographic projections. This approach to HDR tomography has been inspired by HDR…
Let $\mathcal R$ denote the generalized Radon transform (GRT), which integrates over a family of $N$-dimensional smooth submanifolds $\mathcal S_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcal U\subset\mathbb R^n$…
Robustness of deep learning methods for limited angle tomography is challenged by two major factors: a) due to insufficient training data the network may not generalize well to unseen data; b) deep learning methods are sensitive to noise.…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…
Medical imaging is nowadays a pillar in diagnostics and therapeutic follow-up. Current research tries to integrate established - but ionizing - tomographic techniques with technologies offering reduced radiation exposure. Diffuse Optical…
We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can…
Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively…
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…
Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. The corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the…
Although deep learning (DL) has received much attention in accelerated magnetic resonance imaging (MRI), recent studies show that tiny input perturbations may lead to instabilities of DL-based MRI reconstruction models. However, the…
Limited-angle X-ray tomography reconstruction is an ill-conditioned inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical…
Synchrotron radiation sources are widely used in various fields, among which computed tomography (CT) is one of the most important. The amount of effort expended by the operator varies depending on the subject. If the number of angles…
Image restoration methods are commonly used to improve the quality of astronomical images. In recent years, developments of deep neural networks and increments of the number of astronomical images have evoked a lot of data--driven image…
Low dose computed tomography (CT) acquisition using reduced radiation or sparse angle measurements is recommended to decrease the harmful effects of X-ray radiation. Recent works successfully apply deep networks to the problem of low dose…