Related papers: Automatic regularization parameter choice for tomo…

Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov…

The reconstruction of images from measured data is an increasing field of research. For highly under-determined problems, template-based image reconstruction provides a way of compensating for the lack of sufficient data. A caveat of this…

We propose a method for fast and automatic estimation of spatially dependent regularization maps for total variation-based (TV) tomography reconstruction. The estimation is based on two distinct sub-networks, with the first sub-network…

We propose a model-based image reconstruction method for photoacoustic tomography(PAT) involving a novel form of regularization and demonstrate its ability to recover good quality images from significantly reduced size datasets. The…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

Choosing the regularization parameter for inverse problems is of major importance for the performance of the regularization method. We will introduce a fast version of the Lepskij balancing principle and show that it is a valid parameter…

The explorations of models beyond the Standard Model (BSM) naturally involve scans over the unknown BSM parameters. On the other hand, high precision predictions require calculations at the loop-level and thus a renormalization of (some of)…

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce…

This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…

In this work we consider the problem of finding optimal regularization parameters for general-form Tikhonov regularization using training data. We formulate the general-form Tikhonov solution as a spectral filtered solution using the…

Recent years have seen growing interest in exploiting dual- and multi-energy measurements in computed tomography (CT) in order to characterize material properties as well as object shape. Material characterization is performed by…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…

Regularization is a popular technique in machine learning for model estimation and avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data…

We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…

The throughout knowledge of a X-ray beam spectrum is mandatory to assess the quality of its source device. Since the techniques to directly measurement such spectra are expensive and laborious, the X-ray spectrum reconstruction using…

We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…