相关论文: GMRES Methods for Tomographic Reconstruction with …

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging.…

Data-driven deep learning has been successfully applied to various computed tomographic reconstruction problems. The deep inference models may outperform existing analytical and iterative algorithms, especially in ill-posed CT…

Forward imaging technique is the base of combined method on density reconstruction with the forward calculation and inverse problem solution. In the paper, we introduced the projection equation for the radiographic system with areal source…

Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods…

This work considers the convergence of GMRES for non-singular problems. GMRES is interpreted as the GCR method which allows for simple proofs of the convergence estimates. Preconditioning and weighted norms within GMRES are considered. The…

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map…

Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…

Computed tomography (CT) uses X-ray measurements taken from sensors around the body to generate tomographic images of the human body. Conventional reconstruction algorithms can be used if the X-ray data are adequately sampled and of high…

For single source helical Computed Tomography (CT), both Filtered-Back Projection (FBP) and statistical iterative reconstruction have been investigated. However for dual source CT with flying focal spot (DS-FFS CT), statistical iterative…

Phase-wrapping artifacts, statistical image noise and the need for a minimum amount of phase steps per projection limit the practicability of x-ray grating based phase-contrast tomography, when using filtered back projection reconstruction.…

GMRES is a popular Krylov subspace method for solving linear systems of equations involving a general non-Hermitian coefficient matrix. The conventional bounds on GMRES convergence involve polynomial approximation problems in the complex…

As the need for computational power and efficiency rises, parallel systems become increasingly popular among various scientific fields. While multiple core-based architectures have been the center of attention for many years, the rapid…

With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of least squares (LS) problems $\min_x\|b-Ax\|_2$, where $A…

A conventional approach to computed tomography (CT) or cone beam CT (CBCT) metal artifact reduction is to replace the X-ray projection data within the metal trace with synthesized data. However, existing projection or sinogram completion…

In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…

Polynomial convergence bounds are considered for left, right, and split preconditioned GMRES. They include the cases of Weighted and Deflated GMRES for a linear system Ax = b. In particular, the case of positive definite A is considered.…

Machine learning models are commonly trained end-to-end and in a supervised setting, using paired (input, output) data. Examples include recent super-resolution methods that train on pairs of (low-resolution, high-resolution) images.…

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

Constructing 3D representations of object geometry is critical for many robotics tasks, particularly manipulation problems. These representations must be built from potentially noisy partial observations. In this work, we focus on the…

Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…