Related papers: Total-variation regularization strategies in full-…
We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve $L_1$/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our…
Geophysical models usually contain both sharp interfaces and smooth variations, and it is difficult to accurately account for both of these two types of medium parameter variations using conventional full-waveform inversion methods. In…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
We propose a formulation of full-wavefield inversion (FWI) as a constrained optimization problem, and describe a computationally efficient technique for solving constrained full-wavefield inversion (CFWI). The technique is based on using a…
Total variation regularization has proven to be a valuable tool in the context of optimal control of differential equations. This is particularly attributed to the observation that TV-penalties often favor piecewise constant minimizers with…
This paper proposes a computationally efficient algorithm to address the Full-Waveform Inversion (FWI) problem with a Total Variation (TV) constraint, designed to accurately reconstruct subsurface properties from seismic data. FWI, as an…
Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be easily trapped in a local minimum. On the other hand, the inversion results may exhibit strong artifacts and reduced resolution because of…
In a recent paper by A. Chambolle et al. [Geometric properties of solutions to the total variation denoising problem. Inverse Problems 33, 2017] it was proven that if the subgradient of the total variation at the noise free data is not…
This paper provides a new algorithm for solving inverse problems, based on the minimization of the $L^2$ norm and on the control of the Total Variation. It consists in relaxing the role of the Total Variation in the classical Total…
We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total…
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…
This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…
An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…
This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…
The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
In this work we analyze the Total Variation-Wasserstein minimization problem. We propose an alternative form of deriving optimality conditions from the approach of Calier\&Poon'18, and as result obtain further regularity for the quantities…
Scarcity of hydrocarbon resources and high exploration risks motivate the development of high fidelity algorithms and computationally viable approaches to exploratory geophysics. Whereas early approaches considered least-squares…