相关论文: Towards a Mathematical Theory of Super-Resolution

In this paper, we propose a novel approach to hyperspectral image super-resolution by modeling the global spatial-and-spectral correlation and local smoothness properties over hyperspectral images. Specifically, we utilize the tensor…

Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…

Super-Resolution (SR) is the problem that consists in reconstructing images that have been degraded by a zoom-out operator. This is an ill-posed problem that does not have a unique solution, and numerical approaches rely on a prior on…

I explain what is, what is not, and what is only sort of superresolution microscopy. I discuss optical resolution, first in terms of diffraction theory, then in terms of linear systems theory, and finally in terms of techniques that use…

We address the ambiguities in the super-resolution problem under translation. We demonstrate that combinations of low-resolution images at different scales can be used to make the super-resolution problem well posed. Such differences in…

In this paper we aim to tackle the problem of reconstructing a high-resolution image from a single low-resolution input image, known as single image super-resolution. In the literature, sparse representation has been used to address this…

Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…

We introduce a new audio processing technique that increases the sampling rate of signals such as speech or music using deep convolutional neural networks. Our model is trained on pairs of low and high-quality audio examples; at test-time,…

We investigate the recovery of nodes and amplitudes from noisy frequency samples in spike train signals, also known as the super-resolution (SR) problem. When the node separation falls below the Rayleigh limit, the problem becomes…

This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…

We address the problem of simultaneously recovering a sequence of point source signals from observations limited to the low-frequency end of the spectrum of their summed convolution, where the point spread functions (PSFs) are unknown. By…

This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the…

We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled, and noisy observations. We focus on the low SNR regime, and show that a signal in $\mathbb{R}^M$ is uniquely…

Blind super-resolution can be cast as a low rank matrix recovery problem by exploiting the inherent simplicity of the signal and the low dimensional structure of point spread functions. In this paper, we develop a simple yet efficient…

Surveillance scenarios are prone to several problems since they usually involve low-resolution footage, and there is no control of how far the subjects may be from the camera in the first place. This situation is suitable for the…

This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…

Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…

In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…

In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact…