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This paper presents a novel context-aware image denoising algorithm that combines an adaptive image smoothing technique and color reduction techniques to remove perturbation from adversarial images. Adaptive image smoothing is achieved…
Digital communication systems inherently operate through physical media governed by partial differential equations (PDEs). In this paper, we introduce a physics-aware decoding framework that integrates gradient descent-based error…
We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued with growth conditions formulated with help of an $x-$dependent $N-$function. The main novelty of the paper consists in the lack of…
We describe a rational approach to reduce the computational and communication complexities of lossless point-to-point compression for computation with side information. The traditional method relies on building a characteristic graph with…
We present here a new image inpainting algorithm based on the Sobolev gradient method in conjunction with the Navier-Stokes model. The original model of Bertalmio et al is reformulated as a variational principle based on the minimization of…
We implement stacked denoising autoencoders, a class of neural networks that are capable of learning powerful representations of high dimensional data. We describe stochastic gradient descent for unsupervised training of autoencoders, as…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical…
An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…
We study linear abstract differential-algebraic equations (ADAEs), and we introduce an index concept which is based on polynomial growth of a~pseudo-resolvent. Our approach to solvability analysis is based on degenerate semigroups. We apply…
This letter introduces a physics-informed self-supervised framework for sonar image despeckling that reformulates despeckling as residual consistency in the homomorphic log domain. By constraining the log-ratio residual to obey…
We formulate a framework of polynomial diagrams, which are a generalisation of power diagrams (PDs) and anisotropic power diagrams (APDs) allowing for boundaries between cells to be algebraic curves of a prescribed degree. We show that they…
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
We investigate the automatic differentiation of dominant eigensolver where only a small proportion of eigenvalues and corresponding eigenvectors are obtained. Backpropagation through the dominant eigensolver involves solving certain…
The optimization of physical parameters serves various purposes, such as system identification and efficiency in developing devices. Spin-torque oscillators have been applied to neuromorphic computing experimentally and theoretically, but…
The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape of individual grains. One major obstacle to the wider adoption of APDs is the computational cost…
This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact graph cut optimization techniques. Although isotropic in theory,…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…