Related papers: Optimising Spatial and Tonal Data for PDE-based In…
In this paper, we focus on learning optimal parameters for PDE-based image regularization and decomposition. First we learn the regularization parameter and the differential operator for gray-scale image denoising using the fractional…
Transformations for enhancing sparsity in the approximation of color images by 2D atomic decomposition are discussed. The sparsity is firstly considered with respect to the most significant coefficients in the wavelet decomposition of the…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
Image foreground extraction is a classical problem in image processing and vision, with a large range of applications. In this dissertation, we focus on the extraction of text and graphics in mixed-content images, and design novel…
In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…
Reconstructing high-dimensional spatiotemporal fields from sparse point-sensor measurements is a central challenge in learning parametric PDE dynamics. Existing approaches often struggle to generalize across trajectories and parameter…
The goal of image harmonization is to adjust the foreground in a composite image to achieve visual consistency with the background. Recently, latent diffusion model (LDM) are applied for harmonization, achieving remarkable results. However,…
We propose a noise reduction method for unsteady pressure-sensitive paint (PSP) data based on modal expansion, the coefficients of which are determined from time-series data at optimally placed points. In this study, the proper orthogonal…
Diffusion models excel at joint pixel sampling for image generation but lack efficient training-free methods for partial conditional sampling (e.g., inpainting with known pixels). Prior work typically formulates this as an intractable…
We deal with the problem of sparsity-based audio inpainting, i.e. filling in the missing segments of audio. A consequence of the approaches based on mathematical optimization is the insufficient amplitude of the signal in the filled gaps.…
We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…
In recent years, partial differential equation (PDE) systems have been successfully applied to the binarization of text images, achieving promising results. Inspired by the DH model and incorporating a novel image modeling approach, this…
Large-dimensional empirical data in science and engineering frequently have a low-rank structure and can be represented as a combination of just a few eigenmodes. Because of this structure, we can use just a few spatially localized sensor…
In the image inpainting task, the ability to repair both high-frequency and low-frequency information in the missing regions has a substantial influence on the quality of the restored image. However, existing inpainting methods usually fail…
This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective…
This report describes the experimental analysis of proposed underwater image enhancement algorithms based on partial differential equations (PDEs). The algorithms perform simultaneous smoothing and enhancement due to the combination of both…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
There is a rising interest in Spatio-temporal systems described by Partial Differential Equations (PDEs) among the control community. Not only are these systems challenging to control, but the sizing and placement of their actuation is an…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…