Related papers: Variational regularization of complex deautoconvol…
Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, a convex relaxation of the otherwise nonconvex Tikhonov-regularization for denoising circle-valued data has been…
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…
We address the image restoration problem under Poisson noise corruption. The Kullback-Leibler divergence, which is typically adopted in the variational framework as data fidelity term in this case, is coupled with the second-order Total…
We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods…
Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting, we…
In this paper, a two-step regularization method is used to solve an ill-posed spherical pseudo-differential equation in the presence of noisy data. For the first step of regularization we approximate the data by means of a spherical…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Dusty star-forming galaxies (DSFGs) dominate the far-infrared and sub-millimetre number counts, but single-dish surveys suffer from poor angular resolution, complicating mult-wavelength counterpart identification. Prior-driven deblending…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
Solution of the discretized Lippmann-Schwinger equation in the spatial frequency domain involves the inversion of a linear operator specified by the scattering potential. To regularize this inevitably ill-conditioned problem, we propose a…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
In recent years, tensor decomposition-based approaches for hyperspectral anomaly detection (HAD) have gained significant attention in the field of remote sensing. However, existing methods often fail to fully leverage both the global…
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…
Unified image restoration is a significantly challenging task in low-level vision. Existing methods either make tailored designs for specific tasks, limiting their generalizability across various types of degradation, or rely on training…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
We present a novel self-referenced method for the complete temporal characterization (phase and amplitude) of ultrashort optical laser pulses. The technique, called TIme-Gated Electric field Reconstruction (TIGER), measures a second-order…
Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…