Related papers: Optimal Interpolation Data for PDE-based Compressi…
Autoencoders represent an effective approach for computing the underlying factors characterizing datasets of different types. The latent representation of autoencoders have been studied in the context of enabling interpolation between data…
Inpainting-based codecs store sparse, quantised pixel data directly and decode by interpolating the discarded image parts. This interpolation can be used simultaneously for efficient coding by predicting pixel data to be stored. Such joint…
Compressed sensing is an image reconstruction technique to achieve high-quality results from limited amount of data. In order to achieve this, it utilizes prior knowledge about the samples that shall be reconstructed. Focusing on image…
Discrete empirical interpolation method (DEIM) estimates a function from its incomplete pointwise measurements. Unfortunately, DEIM suffers large interpolation errors when few measurements are available. Here, we introduce Sparse DEIM…
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
Deformable Parts Models and Convolutional Networks each have achieved notable performance in object detection. Yet these two approaches find their strengths in complementary areas: DPMs are well-versed in object composition, modeling…
High levels of noise usually exist in today's captured images due to the relatively small sensors equipped in the smartphone cameras, where the noise brings extra challenges to lossy image compression algorithms. Without the capacity to…
Image denoising aims to remove noise while preserving structural details and perceptual realism, yet distortion-driven methods often produce over-smoothed reconstructions, especially under strong noise and distribution shift. This paper…
Estimating shape and appearance of a three dimensional object from a given set of images is a classic research topic that is still actively pursued. Among the various techniques available, PS is distinguished by the assumption that the…
Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…
Harmonic inpainting with optimised data is very popular for inpainting-based image compression. We improve this approach in three important aspects. Firstly, we replace the standard finite differences discretisation by a finite element…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
Speckle noise severely limits the quality of images acquired from coherent imaging systems such as Synthetic Aperture Radar (SAR) and medical ultrasound. Traditional second-order PDE-based despeckling approaches, although popular, often…
Current self-supervised denoising techniques achieve impressive results, yet their real-world application is frequently constrained by substantial computational and memory demands, necessitating a compromise between inference speed and…
Most problems involving simultaneous localization and mapping can nowadays be solved using one of two fundamentally different approaches. The traditional approach is given by a least-squares objective, which minimizes many local photometric…
A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…
Airborne laser scanning and photogrammetry are two main techniques to obtain 3D data representing the object surface. Due to the high cost of laser scanning, we want to explore the potential of using point clouds derived by dense image…
Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the…
Functions with jumps and kinks typically arising from parameter dependent or stochastic hyperbolic PDEs are notoriously difficult to approximate. If the jump location in physical space is parameter dependent or random, standard…