相关论文: Tomographic inversion using $\ell_1$-norm regulari…

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity regularization does not necessarily produce adequate results…

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

The convergence rates results in $\ell^1$-regularization when the sparsity assumption is narrowly missed, presented by Burger et al. (2013 Inverse Problems 29 025013), are based on a crucial condition which requires that all basis elements…

Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation…

Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…

In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging,…

Classically, anisotropic surface wave tomography is treated as an optimisation problem where it proceeds through a linearised two-step approach. It involves the construction of 2D group or phase velocity maps for each considered period,…

1. Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative…

Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some…

The inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term that incorporates prior knowledge about the underlying…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted $\ell_1$ algorithms for solving $\ell_p$ regularization problems, which are widely applied for inducing sparse solutions. We show that if…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…