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Found 14 papers, 5 papers with code
Proximal methods for point source localisation
Point source localisation is generally modelled as a Lasso-type problem on measures.
Non-planar sensing skins for structural health monitoring based on electrical resistance tomography
Electrical resistance tomography (ERT) -based distributed surface sensing systems, or sensing skins, offer alternative sensing techniques for structural health monitoring, providing capabilities for distributed sensing of, for example, damage, strain and temperature.
Image Reconstruction
Computational Physics
Numerical Analysis
Differential Geometry
Numerical Analysis
Inverse problems with second-order Total Generalized Variation constraints
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations.
Predictive online optimisation with applications to optical flow
To prove convergence we need a predictor for the dual variable based on (proximal) gradient flow.
Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization
We demonstrate that difficult non-convex non-smooth optimization problems, such as Nash equilibrium problems and anisotropic as well as isotropic Potts segmentation model, can be written in terms of generalized conjugates of convex functionals.
Optimization and Control
Acceleration and global convergence of a first-order primal--dual method for nonconvex problems
The primal--dual hybrid gradient method (PDHGM, also known as the Chambolle--Pock method) has proved very successful for convex optimization problems involving linear operators arising in image processing and inverse problems.
Optimization and Control
Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization
We study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces.
Optimization and Control
Acceleration of the PDHGM on strongly convex subspaces
We propose several variants of the primal-dual method due to Chambolle and Pock.
Diffusion tensor imaging with deterministic error bounds
Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices.
The structure of optimal parameters for image restoration problems
The analysis is done on the original -- in image restoration typically non-smooth variational problem -- as well as on a smoothed approximation set in Hilbert space which is the one considered in numerical computations.
Bilevel approaches for learning of variational imaging models
We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space.
The jump set under geometric regularisation. Part 2: Higher-order approaches
In Part 1, we developed a new technique based on Lipschitz pushforwards for proving the jump set containment property $\mathcal{H}^{m-1}(J_u \setminus J_f)=0$ of solutions $u$ to total variation denoising.
The jump set under geometric regularisation. Part 1: Basic technique and first-order denoising
Their proof unfortunately depends heavily on the co-area formula, as do many results in this area, and as such is not directly extensible to higher-order, curvature-based, and other advanced geometric regularisers, such as total generalised variation (TGV) and Euler's elastica.
Imaging with Kantorovich-Rubinstein discrepancy
We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems.
