Related papers: TV-regularized CT Reconstruction and Metal Artifac…
This paper proposes a sinogram consistency learning method to deal with beam-hardening related artifacts in polychromatic computerized tomography (CT). The presence of highly attenuating materials in the scan field causes an inconsistent…
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…
In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…
Direct reconstruction through filtered back projection engenders metal artifacts in polychromatic computed tomography images, attributed to highly attenuating implants, which further poses great challenges for subsequent image analysis.…
We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV)…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
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…
This paper provides a new algorithm for solving inverse problems, based on the minimization of the $L^2$ norm and on the control of the Total Variation. It consists in relaxing the role of the Total Variation in the classical Total…
Purpose: There is growing interest in the use of modern 3D printing technology to implement intensity-modulated radiation therapy (IMRT) on the preclinical scale which is analogous to clinical IMRT. However, current 3D-printed IMRT methods…
In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…
In recent works several authors have proposed the use of precise boundary conditions (BCs) for blurring models and they proved that the resulting choice (Neumann or reflective, anti-reflective) leads to fast algorithms both for deblurring…
We introduce a novel regulariser based on the natural vector field operations gradient, divergence, curl and shear. For suitable choices of the weighting parameters contained in our model it generalises well-known first- and second-order…
Modern tomography involves gathering projection data from multiple directions and feeding them into a software algorithm for tomographic reconstruction. We focus our study on image reconstruction from Radon data in the setting of…
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space…
In Cone-Beam CT (CBCT) imaging systems, the scattering phenomenon has a significant impact on the reconstructed image and is a long-lasting research topic on CBCT. In this paper, we propose a simple, novel and fast approach for mitigating…
This paper is concerned with an elliptic optimal control problem with total variation (TV) restriction on the control in the constraints. We introduce a regularized optimal control problem by applying a quadratic regularization of the dual…
We present a note on the implementation and efficacy of a box-constrained $L_1/L_2$ regularization in numerical optimization approaches to performing tomographic reconstruction from a single projection view. The constrained $L_1/L_2$…
This work proposes the variable exponent Lebesgue modular as a replacement for the 1-norm in total variation (TV) regularization. It allows the exponent to vary with spatial location and thus enables users to locally select whether to…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…