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In this paper we consider the mathematical model of thermo- and photo-acoustic tomography for the recovery of the initial condition of a wave field from knowledge of its boundary values. Unlike the free-space setting, we consider the wave…
This paper introduces a novel mathematical property applicable to diverse images, referred to as FINOLA (First-Order Norm+Linear Autoregressive). FINOLA represents each image in the latent space as a first-order autoregressive process, in…
Images encode both the state of the world and its content. The former is useful for tasks such as planning and control, and the latter for classification. The automatic extraction of this information is challenging because of the…
In a given scene, humans can often easily predict a set of immediate future events that might happen. However, generalized pixel-level anticipation in computer vision systems is difficult because machine learning struggles with the…
Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…
This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…
Inpainting-based compression represents images in terms of a sparse subset of its pixel data. Storing the carefully optimised positions of known data creates a lossless compression problem on sparse and often scattered binary images. This…
We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…
Underwater video pairs are fairly difficult to obtain due to the complex underwater imaging. In this case, most existing video underwater enhancement methods are performed by directly applying the single-image enhancement model frame by…
Image of a scene captured through a piece of transparent and reflective material, such as glass, is often spoiled by a superimposed layer of reflection image. While separating the reflection from a familiar object in an image is mentally…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
The ever-growing amounts of visual contents captured on a daily basis necessitate the use of lossy compression methods in order to save storage space and transmission bandwidth. While extensive research efforts are devoted to improving…
Intrinsic image decomposition, which is an essential task in computer vision, aims to infer the reflectance and shading of the scene. It is challenging since it needs to separate one image into two components. To tackle this, conventional…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
Rotation invariance has been studied in the computer vision community primarily in the context of small in-plane rotations. This is usually achieved by building invariant image features. However, the problem of achieving invariance for…
Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this work we show that those properties uniquely define an {\em intrinsic wavelet} and present a suitable…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
We present a novel method for predicting accurate depths from monocular images with high efficiency. This optimal efficiency is achieved by exploiting wavelet decomposition, which is integrated in a fully differentiable encoder-decoder…
Generating image variations, where a model produces variations of an input image while preserving the semantic context has gained increasing attention. Current image variation techniques involve adapting a text-to-image model to reconstruct…