Related papers: Optimal Interpolation Data for PDE-based Compressi…

Statistical shape models (SSM) have been well-established as an excellent tool for identifying variations in the morphology of anatomy across the underlying population. Shape models use consistent shape representation across all the samples…

We consider the very challenging task of restoring images (i) which have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise and (iii) the ideal image to be restored contains both cartoon and texture…

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…

Removing noise from images is a challenging and fundamental problem in the field of computer vision. Images captured by modern cameras are inevitably degraded by noise which limits the accuracy of any quantitative measurements on those…

A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…

Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…

We present an initial implementation of a probabilistic PDE-constrained shape optimization algorithm. Our method is based on a novel probabilistic representation of the shape derivative, which is evaluated using Monte Carlo sampling; and…

We propose a new grayscale image denoiser, dubbed as Neural Affine Image Denoiser (Neural AIDE), which utilizes neural network in a novel way. Unlike other neural network based image denoising methods, which typically apply simple…

We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…

Most of today's state-of-the-art methods for perspective shape from shading are modelled in terms of partial differential equations (PDEs) of Hamilton-Jacobi type. To improve the robustness of such methods w.r.t. noise and missing data,…

Infrared and visible image fusion aims to generate synthetic images simultaneously containing salient features and rich texture details, which can be used to boost downstream tasks. However, existing fusion methods are suffering from the…

The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…

Existing denoising methods typically restore clear results by aggregating pixels from the noisy input. Instead of relying on hand-crafted aggregation schemes, we propose to explicitly learn this process with deep neural networks. We present…

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…

Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction, deformable image registration, atlas-based segmentation,…

We explore the connection between Plug-and-Play (PnP) methods and Denoising Diffusion Implicit Models (DDIM) for solving ill-posed inverse problems, with a focus on single-pixel imaging. We begin by identifying key distinctions between PnP…

The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models,…

We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…

In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…