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Computed Tomography (CT) reconstruction is a fundamental component to a wide variety of applications ranging from security, to healthcare. The classical techniques require measuring projections, called sinograms, from a full 180$^\circ$…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
Computed tomography (CT) is a widely-used imaging technology that assists clinical decision-making with high-quality human body representations. To reduce the radiation dose posed by CT, sparse-view and limited-angle CT are developed with…
In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests…
The use of ray projections to reconstruct images is a common technique in medical imaging. Dealing with incomplete data is particularly important when a patient is vulnerable to potentially damaging radiation or is unable to cope with the…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
Computed Tomography (CT) is pivotal in industrial quality control and medical diagnostics. Sparse-view CT, offering reduced ionizing radiation, faces challenges due to its under-sampled nature, leading to ill-posed reconstruction problems.…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods…
The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…
A major challenge in computed tomography (CT) is to reduce X-ray dose to a low or even ultra-low level while maintaining the high quality of reconstructed images. We propose a new method for CT reconstruction that combines penalized…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
Differential phase contrast interior tomography allows for reconstruction of a refractive index distribution over a region of interest (ROI) for visualization and analysis of internal structures inside a large biological specimen. In this…
The diagnostic quality of computed tomography (CT) scans is usually restricted by the induced patient dose, scan speed, and image quality. Sparse-angle tomographic scans reduce radiation exposure and accelerate data acquisition, but suffer…
As the medical usage of computed tomography (CT) continues to grow, the radiation dose should remain at a low level to reduce the health risks. Therefore, there is an increasing need for algorithms that can reconstruct high-quality images…
A new method for reducing metal artifacts in X-ray computed tomography (CT) images is presented. It bases on the solution of a convex optimization problem with inequality constraints on the sinogram, and total variation regularization for…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
Purpose: We develop an iterative image-reconstruction algorithm for application to low-intensity computed tomography (CT) projection data, which is based on constrained, total-variation (TV) minimization. The algorithm design focuses on…