Related papers: Superresolution without Separation
We present the development of extended diffraction tomography, a new approach to the solution of the linear seismic waveform inversion problem. This method has several appealing features, such as the use of arbitrary depth-dependent…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
The multichannel trigonometric reconstruction from uniform samples was proposed recently. It not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according…
Fluorescence microscopy is a critical tool across various disciplines, from materials science to biomedical research, yet it is limited by the diffraction limit of resolution. Advanced super-resolution techniques such as localization…
Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
Seismic full-waveform inversion is a core technology for obtaining high-resolution subsurface model parameters. However, its highly nonlinear characteristics and strong dependence on the initial model often lead to the inversion process…
Modern radio interferometers deliver large volumes of data containing high-sensitivity sky maps over wide fields-of-view. These large area observations can contain various and superposed structures such as point sources, extended objects,…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Highest resolution imaging in astronomy is achieved by interferometry, connecting telescopes over increasingly longer distances, and at successively shorter wavelengths. Here, we present the first diffraction-limited images in visual light,…
Single-channel audio separation aims to separate individual sources from a single-channel mixture. Most existing methods rely on supervised learning with synthetically generated paired data. However, obtaining high-quality paired data in…
Image Phase Alignment Super-sampling (ImPASS) is a computational method for combining displaced low-resolution images into a single high-resolution image. The general steps include measuring the relative displacements, up-sampling, aligning…
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…
This work presents a new super-resolution imaging approach by using subwavelength hole resonances. We employ a subwavelength structure in which an array of tiny holes are etched in a metallic slab with the neighboring distance $\ell$ that…
Particle tracking in biological imaging is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles. The standard approach of particle tracking consists of two steps: first reconstructing…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
We present a novel approach to leverage prior knowledge encapsulated in pre-trained text-to-image diffusion models for blind super-resolution (SR). Specifically, by employing our time-aware encoder, we can achieve promising restoration…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
In this paper, we show by experiment that by covering a thin flat nonlinear lens on the sources, the sub-diffraction-limit observation can be achieved by measuring either the near-field distribution or the far-field radiation of the sources…
Image hallucination and super-resolution have been studied for decades, and many approaches have been proposed to upsample low-resolution images using information from the images themselves, multiple example images, or large image…