Related papers: Sobolev gradients and image interpolation
The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…
Image inpainting is a restoration process which has numerous applications. Restoring of scanned old images with scratches, or removing objects in images are some of inpainting applications. Different approaches have been used for…
We propose a new gradient-domain technique for processing registered EM image stacks to remove inter-image discontinuities while preserving intra-image detail. To this end, we process the image stack by first performing anisotropic…
We extend the result on the spectral projected gradient method by Birgin et al. in 2000 to a log-determinant semidefinite problem (SDP) with linear constraints and propose a spectral projected gradient method for the dual problem. Our…
This paper concerns an optimization algorithm for unconstrained non-convex problems where the objective function has sparse connections between the unknowns. The algorithm is based on applying a dissipation preserving numerical integrator,…
In many advanced video based applications background modeling is a pre-processing step to eliminate redundant data, for instance in tracking or video surveillance applications. Over the past years background subtraction is usually based on…
This paper proposes a novel stroke-based rendering (SBR) method that translates images into vivid oil paintings. Previous SBR techniques usually formulate the oil painting problem as pixel-wise approximation. Different from this technique…
We introduce a new class of swarm-based inertial methods (SBIMs) for global minimization, formulated as coupled dissipative inertial dynamical systems derived from the generalized Onsager principle. The proposed framework identifies the…
We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method…
This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…
Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…
Image inpainting involves filling in damaged or missing regions of an image by utilizing information from the surrounding areas. In this paper, we investigate a highly nonlinear partial differential equation inspired by the modified…
We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence…
A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…
We consider the incompressible and stationary Stokes equations on an infinite two-dimensional wedge with non-scaling invariant Navier-slip boundary conditions. We prove well-posedness and higher regularity of the Stokes problem in a certain…
In this paper, we focus on image inpainting task, aiming at recovering the missing area of an incomplete image given the context information. Recent development in deep generative models enables an efficient end-to-end framework for image…
This paper introduces a novel watermarking method for diffusion models. It is based on guiding the diffusion process using the gradient computed from any off-the-shelf watermark decoder. The gradient computation encompasses different image…
We investigate theoretically and numerically the use of the Least-Squares Finite-element method (LSFEM) to approach data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is based…
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…
Combining the properties of monovariate internal functions as proposed in Kolmogorov superimposition theorem, in tandem with the bounds wielded by the multivariate formulation of Chebyshev inequality, a hybrid model is presented, that…