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Modern optical systems are subject to very restrictive performance, size and cost requirements. Especially in portable systems size often is the most important factor, which necessitates elaborate designs to achieve the desired…

Recently, many deep image compression methods have been proposed and achieved remarkable performance. However, these methods are dedicated to optimizing the compression performance and speed at medium and high bitrates, while research on…

Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of…

With the great success of diffusion models in image generation, diffusion-based image compression is attracting increasing interests. However, due to the random noise introduced in the diffusion learning, they usually produce…

Increasingly, visual signals such as images, videos and point clouds are being captured solely for the purpose of automated analysis by computer vision models. Applications include traffic monitoring, robotics, autonomous driving, smart…

The field of neural image compression has witnessed exciting progress as recently proposed architectures already surpass the established transform coding based approaches. While, so far, research has mainly focused on architecture and model…

In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…

We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…

Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…

This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…

Transformations for enhancing sparsity in the approximation of color images by 2D atomic decomposition are discussed. The sparsity is firstly considered with respect to the most significant coefficients in the wavelet decomposition of the…

We propose a new approach to the problem of optimizing autoencoders for lossy image compression. New media formats, changing hardware technology, as well as diverse requirements and content types create a need for compression algorithms…

This work investigates functional source coding problems with maximal distortion, motivated by approximate function computation in many modern applications. The maximal distortion treats imprecise reconstruction of a function value as good…

In cold atomic systems, fast and high-resolution microscopy of individual atoms is crucial, since it can provide direct information on the dynamics and correlations of the system. Here, we demonstrate nanosecond-scale two-dimensional…

To overcome the limit of diffraction while achieving the superresolution technique, solid immersion lenses are the key optical elements for data storage and nanophotonics applications. Recent demonstrations have shown how different…

We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…

In this study, we propose a novel scheme for systematic improvement of lossless image compression coders from the point of view of the universal codes in information theory. In the proposed scheme, we describe a generative model class of…

By introducing a new operator theory, we provide a unified mathematical theory for general source resolution in the multi-illumination imaging problem. Our main idea is to transform multi-illumination imaging into single-snapshot imaging…

We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…

We determine the bound to the maximum achievable sensitivity in the estimation of a scalar parameter from the information contained in an optical image in the presence of quantum noise. This limit, based on the Cramer-Rao bound, is valid…