Related papers: Blind inverse problems with isolated spikes
This paper defines a novel Bayesian inverse problem to infer an infinite-dimensional uncertain operator appearing in a differential equation, whose action on an observable state variable affects its dynamics. Inference is made tractable by…
Minimum phase functions are fundamental in a range of applications, including control theory, communication theory and signal processing. A basic mathematical challenge that arises in the context of geophysical imaging is to understand the…
As handheld video cameras are now commonplace and available in every smartphone, images and videos can be recorded almost everywhere at anytime. However, taking a quick shot frequently yields a blurry result due to unwanted camera shake…
This work is concerned with the problem of blind source separation and its applications to imaging. We first establish a theoretical result that we stated in our previous article on imaging in diffusive environments. This result is a…
Optical imaging systems are inherently imperfect due to diffraction limits, lens manufacturing tolerances, assembly misalignment, and other physical constraints. In addition, unavoidable camera shake and object motion further introduce…
The inverse nodal problem for Dirac type integro-differential operator with the spectral parameter in the boundary conditions is studied. We prove that dense subset of the nodal points determines the coefficients of differential part of…
We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and…
The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…
One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. The current paper is concerned with the invariance of Modular biframes for operators under some class of…
We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is…
Recovering radiometric fidelity from unknown dynamic range compression (UDRC), such as low-light enhancement and HDR reconstruction, is a challenging blind inverse problem, due to the unknown forward model and irreversible information loss…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…
We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible.…
Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the…
We consider second order linear differential operators possessing a term depending on the unknown function with a fixed argument and study the uniqueness of recovering the operators from the spectrum. We also obtain a constructive procedure…