Related papers: A unified method for super-resolution recovery and…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
Super-resolution is generally referred to as the task of recovering fine details from coarse information. Motivated by applications such as single-molecule imaging, radar imaging, etc., we consider parameter estimation of complex…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…
Several problems in signal processing are addressed by expert systems which take into account a set of priors on the sought signals and systems. For instance, blind source separation is often tackled by means of a mono-objective formulation…
We revisit the source image estimation problem from blind source separation (BSS). We generalize the traditional minimum distortion principle to maximum likelihood estimation with a model for the residual spectrograms. Because residual…
Super-resolution is a fundamental problem in computer vision which aims to overcome the spatial limitation of camera sensors. While significant progress has been made in single image super-resolution, most algorithms only perform well on…
We present a parameter-decoupled superresolution framework for estimating sub-wavelength separations of passive two-point sources without requiring prior knowledge or control of the source. Our theoretical foundation circumvents the need to…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different band-limited point spread functions, from the observation of their superpositions. This problem arises in…
We propose a method to reconstruct the density of a luminescent source in a highly-scattering medium from ultrasound modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the diffusion…
Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires…
A method for spatial deconvolution of spectra is presented. It follows the same fundamental principles as the ``MCS image deconvolution algorithm'' (Magain, Courbin, Sohy, 1998) and uses information contained in the spectrum of a reference…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
This work is concerned with the problem of blind source separation and its applications to imaging. We first establish a theoretical result that we stated in our previous article on imaging in diffusive environments. This result is a…
This work studies the problem of simultaneously separating and reconstructing signals from compressively sensed linear mixtures. We assume that all source signals share a common sparse representation basis. The approach combines classical…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
Unified image restoration is a significantly challenging task in low-level vision. Existing methods either make tailored designs for specific tasks, limiting their generalizability across various types of degradation, or rely on training…
Structured illumination microscopy (SIM) uses a set of images captured with different illumination patterns to computationally reconstruct resolution beyond the diffraction limit. Here, we propose an alternative approach using a single…
Blind Source Separation (BSS) is a challenging matrix factorization problem that plays a central role in multichannel imaging science. In a large number of applications, such as astrophysics, current unmixing methods are limited since…
Blind source separation (BSS) techniques aims at joint estimation of source signals and a mixing matrix from observations of mixtures. This paper addresses a doubly nonstationary BSS problem, where the mixing matrix is time dependent and…