相关论文: Inversion of the radiative transfer equation for p…
A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical…
Remote sensing of the atmospheres of distant worlds motivates a firm understanding of radiative transfer. In this review, we provide a pedagogical cookbook that describes the principal ingredients needed to perform a radiative transfer…
Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the…
Prompted by the relevant problem of temperature inversion (i.e. gradient of density anti-correlated to the gradient of temperature) in astrophysics, we introduce a novel method to model a gravitationally confined multi-component…
We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
Stellar seismic inversions have proved to be a powerful technique for probing the internal structure of stars, and paving the way for a better understanding of the underlying physics by revealing some of the shortcomings in current stellar…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
Magnetic fields on the surface of the Sun and stars in general imprint or modify the polarization state of the electromagnetic radiation that is leaving from the star. The inference of solar/stellar magnetic fields is performed by…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
The advent of space-based photometry missions in the early 21st century enabled the application to asteroseismic data of advanced inference techniques until then restricted to the field of helioseismology. The high quality of the…
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
An inversion technique has been developed to recover LTE one-dimensional model photospheres for late-type stars from very high-resolution high signal-to-noise stellar line profiles. It is successfully applied to the Sun using a set of…
Inferences of the magnetic field in the solar atmosphere by means of spectropolarimetric inversions (i.e., Stokes inversion codes) yield magnetic fields that are non-solenoidal($\nabla\cdot{\bf B} \ne 0$). Because of this, results obtained…