Related papers: Application of Regularization Methods in the Sky M…
In this paper, we apply our sky map reconstruction method for transit type interferometers to the Tianlai cylinder array. The method is based on the spherical harmonic decomposition, and can be applied to cylindrical array as well as dish…
The Tianlai cylinder array is a pathfinder for developing and testing 21cm intensity mapping techniques. In this paper, we use numerical simulation to assess how its measurement is affected by thermal noise and the errors in calibration and…
The Tianlai Cylinder Pathfinder is a radio interferometer array designed to test techniques for 21 cm intensity mapping in the post-reionization Universe, with the ultimate aim of mapping the large scale structure and measuring cosmological…
The Tianlai Pathfinder is designed to demonstrate the feasibility of using a wide field of view radio interferometers to map the density of neutral hydrogen in the Universe after the Epoch of Reionizaton. This approach, called 21~cm…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
The Tianlai Dish Pathfinder Array is a radio interferometer designed to test techniques for 21~cm intensity mapping in the post-reionization universe as a means for measuring large-scale cosmic structure. It performs drift scans of the sky…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
The spherical harmonics $m$-mode decomposition is a powerful sky map reconstruction method suitable for radio interferometers operating in transit mode. It can be applied to various configurations, including dish arrays and cylinders. We…
Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in…
This paper describes and compares some structure preserving techniques for the solution of linear discrete ill-posed problems with the t-product. A new randomized tensor singular value decomposition (R-tSVD) with a t-product is presented…
We consider the estimation of the regularization parameter for the simultaneous deblurring of multiple noisy images via Tikhonov regularization. We approach the problem in three ways. We first reduce the problem to a single-image deblurring…
Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
Meshless collocation with multiquadric radial basis functions (MQ-RBFs) delivers high accuracy for the three-dimensional Helmholtz equation but produces dense, severely ill-conditioned linear systems. We develop and evaluate three…
Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed…
Airborne transient electromagnetic (TEM) is a cost-effective method to image the distribution of electrical conductivity in the ground. We consider layered earth inversion to interpret large data sets of hundreds of kilometre. Different…
A host of new low-frequency radio telescopes seek to measure the 21-cm transition of neutral hydrogen from the early universe. These telescopes have the potential to directly probe star and galaxy formation at redshifts $20 \gtrsim z…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…