Related papers: Optimal Transport for Super Resolution Applied to …
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…
Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
Ultrasound imaging faces a trade-off between image quality and hardware complexity caused by dense transducers. Sparse arrays are one popular solution to mitigate this challenge. This work proposes an end-to-end optimization framework that…
Recent research has emphasized the benefits of accurately reconstructing the initial Lagrangian positions of biased tracers from their positions at a later time, to gain cosmological information. A weighted semi-discrete optimal transport…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…
Deep convolutional neural networks demonstrate impressive results in the super-resolution domain. A series of studies concentrate on improving peak signal noise ratio (PSNR) by using much deeper layers, which are not friendly to constrained…
Super-resolution and denoising are ill-posed yet fundamental image restoration tasks. In blind settings, the degradation kernel or the noise level are unknown. This makes restoration even more challenging, notably for learning-based…
Resolution enhancements are often desired in imaging applications where high-resolution sensor arrays are difficult to obtain. Many computational imaging methods have been proposed to encode high-resolution scene information on…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…
Heisenberg's uncertainty principle tells us that it is impossible to determine simultaneously the position of a photon crossing a telescope's aperture and its momentum. Super-resolution imaging techniques rely on modification of the…
Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a…
The angular resolution is tha ability of a telescope to render detail: the higher the resolution the finer is the detail. it is, together with the aperture, the most important characteristic of telescopes. We propose a new construction of…
One of the main limitations for the resolution of optical instruments is the size of the sensor's pixels. In this paper we introduce a new sub pixel resolution algorithm to enhance the resolution of images. This method is based on the…