Related papers: Regularization of the Factorization Method applied…
Processing of Diffusion MRI data obtained from High Angular Resolution measurements consists of a series of steps, starting with the estimation of an orientation distribution function (ODF), which is then used as input for e.g. tractography…
Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…
We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain…
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…
In this paper, we formulate the reconstruction problem in diffuse optical tomography (DOT) in a statistical setting for determining the optical parameters, scattering and absorption, from boundary photon density measurements. A special kind…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born…
X-ray tomography is a reliable tool for determining the inner structure of 3D object with penetrating X-rays. However, traditional reconstruction methods such as FDK require dense angular sampling in the data acquisition phase leading to…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
We have shown that the left side null space of the autoregression (AR) matrix operator is the lexicographical presentation of the point spread function (PSF) on condition the AR parameters are common for original and blurred images. The…
X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval…
Normalization methods play an important role in enhancing the performance of deep learning while their theoretical understandings have been limited. To theoretically elucidate the effectiveness of normalization, we quantify the geometry of…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
We introduce a framework for the reconstruction of the amplitude, phase and polarisation of an optical vector-field using calibration measurements acquired by an imaging device with an unknown linear transformation. By incorporating…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…
Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized…
Factorial clustering methods have been developed in recent years thanks to the improving of computational power. These methods perform a linear transformation of data and a clustering on transformed data optimizing a common criterion.…
Boolean matrix factorization is a natural and a popular technique for summarizing binary matrices. In this paper, we study a problem of Boolean matrix factorization where we additionally require that the factor matrices have consecutive…