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We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…
Denoising diffusion probabilistic models have recently received much research attention since they outperform alternative approaches, such as GANs, and currently provide state-of-the-art generative performance. The superior performance of…
Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate…
While CNNs were long considered state of the art for image processing, the introduction of Transformer architectures has challenged this position. While achieving excellent results in image classification and segmentation, Transformers…
We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…
Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number…
In this paper, we introduce a novel approach for active contours with free endpoints. A scheme is presented for image segmentation and restoration based on a discrete version of the Mumford-Shah functional where the contours can be both…
With the successful application of deep learning in communications systems, deep neural networks are becoming the preferred method for signal classification. Although these models yield impressive results, they often come with high…
Models based on deep convolutional networks have dominated recent image interpretation tasks; we investigate whether models which are also recurrent, or "temporally deep", are effective for tasks involving sequences, visual and otherwise.…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
Deep learning solutions of the salient object detection problem have achieved great results in recent years. The majority of these models are based on encoders and decoders, with a different multi-feature combination. In this paper, we show…
We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…
We investigate the conditions under which unconditional dense coding can be achieved using continuous variable entanglement. We consider the effect of entanglement impurity and detector efficiency and discuss experimental verification. We…
In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as…
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…
The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the…
$\ell_1$ based sparse regularization plays a central role in compressive sensing and image processing. In this paper, we propose $\ell_1$DecNet, as an unfolded network derived from a variational decomposition model incorporating $\ell_1$…
Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a…