Related papers: Regularization of the Factorization Method applied…
A fast and robust algorithm for fluorescence diffuse optical tomography is proposed. We identify the location of a fluorescence target by assuming a cuboid. The proposed numerical method is verified by a numerical experiment and an in vivo…
In this paper we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting,…
Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the…
In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
Feature shaping refers to a family of methods that exhibit state-of-the-art performance for out-of-distribution (OOD) detection. These approaches manipulate the feature representation, typically from the penultimate layer of a pre-trained…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid)…
Tomography is a central tool in medical applications, allowing doctors to investigate patients' interior features. The Radon transform (in two dimensions) is commonly used to model the measurement process in parallel-beam CT. Suitable…
Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances…
Factor Analysis is an effective way of dimensionality reduction achieved by revealing the low-rank plus sparse structure of the data covariance matrix. The corresponding model identification task is often formulated as an optimization…
This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…
We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…
Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner. One major drawback of optical diffraction tomography is poor…
Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic…
This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…
In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows…
In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…
Fluorescence molecular tomography (FMT) is an emerging powerful tool for biomedical research. There are two factors that influence FMT reconstruction most effectively. The first one is the regularization techniques. Traditional methods such…