Related papers: What bandwidth do I need for my image?
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…
Many optical measurement techniques, such as light scattering from wavelength-scale particles or detecting motion from a surface with an optical lever, encode information in a complex radiation pattern. Extracting all available information…
Estimating the true background in an astronomical image is fundamental to detecting faint sources. In a typical low-photon count astronomical image, such as in the far and near-ultraviolet wavelength range, conventional methods relying on…
We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical…
Fourier-based optical computing operations, such as spatial differentiation, have recently been realized in compact form factors using flat optics. Experimental demonstrations, however, have been limited to coherent light requiring laser…
A long-standing vision in computer science has been to evolve computing devices into proactive assistants that enhance our productivity, health and wellness, and many other facets of our lives. User digitization is crucial in achieving this…
Incorporating diffusion models in the image compression domain has the potential to produce realistic and detailed reconstructions, especially at extremely low bitrates. Previous methods focus on using diffusion models as expressive…
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of…
In contrast to human vision, common recognition algorithms often fail on partially occluded images. We propose characterizing, empirically, the algorithmic limits by finding a minimal recognizable patch (MRP) that is by itself sufficient to…
The determination of chemical abundances from stellar spectra is considered a mature field of astrophysics. Digital spectra of stars are recorded and processed with standard techniques, much like samples in the biological sciences.…
Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets…
Low-bandwidth communication, such as underwater acoustic communication, is limited by best-case data rates of 30--50 kbit/s. This renders such channels unusable or inefficient at best for single image, video, or other bandwidth-demanding…
It is known that a spatially partially coherent light field produces better imaging contrast compared to a spatially coherent field and that the contrast increases as the spatial coherence length of the field becomes smaller. The transverse…
The fidelity of radio astronomical images is generally assessed by practical experience, i.e. using rules of thumb, although some aspects and cases have been treated rigorously. In this paper we present a mathematical framework capable of…
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays. The size of the smallest bounded…
Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a…
Many visual representations, such as volume-rendered images and metro maps, feature a noticeable amount of information loss. At a glance, there seem to be numerous opportunities for viewers to misinterpret the data being visualized, hence…
We are concerned with numerical simulations of quantum optical circuits under certain realistic conditions, specifically that photon quantum states are not perfectly indistinguishable. The partial photon distinguishability presents a…
In the past years modern mathematical methods for image analysis have led to a revolution in many fields, from computer vision to scientific imaging. However, some recently developed image processing techniques successfully exploited by…
Reducing the data footprint of visual content via image compression is essential to reduce storage requirements, but also to reduce the bandwidth and latency requirements for transmission. In particular, the use of compressed images allows…