相关论文: Mathematical Theory of Computational Resolution Li…
Diffusion models have demonstrated impressive image synthesis performance, yet many UNet-based models are trained at certain fixed resolutions. Their quality tends to degrade when generating images at out-of-training resolutions. We trace…
We consider the problem of recovering a signal consisting of a superposition of point sources from low-resolution data with a cut-off frequency f. If the distance between the sources is under 1/f, this problem is not well posed in the sense…
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…
In this paper, we develop a new technique to obtain nearly optimal estimates of the computational resolution limits introduced in Appl. Comput. Harmon. Anal. 56 (2022) 402-446; IEEE Trans. Inf. Theory 67(7) (2021) 4812-4827; Inverse Probl.…
We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…
Estimating the angular separation between two incoherently radiating monochromatic point sources is a canonical toy problem to quantify spatial resolution in imaging. In recent work, Tsang {\em et al.} showed, using a Fisher Information…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
Most existing super-resolution methods and datasets have been developed to improve the image quality in well-lighted conditions. However, these methods do not work well in real-world low-light conditions as the images captured in such…
We study the problem of simultaneous search for multiple targets over a multidimensional unit cube and derive fundamental resolution limits of non-adaptive querying procedures using the 20 questions estimation framework. The performance…
Super Resolution is the problem of recovering a high-resolution image from a single or multiple low-resolution images of the same scene. It is an ill-posed problem since high frequency visual details of the scene are completely lost in…
Image superresolution involves the processing of an image sequence to generate a still image with higher resolution. Classical approaches, such as bayesian MAP methods, require iterative minimization procedures, with high computational…
Historically, the resolution of optical imaging systems was dictated by diffraction, and the Rayleigh criterion was long considered an unsurpassable limit. In superresolution microscopy, this limit is overcome by manipulating the emission…
Single image super-resolution traditionally assumes spatially-invariant degradation models, yet real-world imaging systems exhibit complex distance-dependent effects including atmospheric scattering, depth-of-field variations, and…
High-resolution radar range profile (RRP) is crucial for accurate target recognition and scene perception. To get a high-resolution RRP, many methods have been developed, such as multiple signal classification (MUSIC), orthogonal matching…
The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…
We study the problem of recovering the common $k$-sized support of a set of $n$ samples of dimension $d$, using $m$ noisy linear measurements per sample. Most prior work has focused on the case when $m$ exceeds $k$, in which case $n$ of the…
This paper presents an innovative approach to computational acoustic imaging of biperiodic surfaces, exploiting the capabilities of an acoustic superlens to overcome the diffraction limit. We address the challenge of imaging physical…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
We consider the two-dimensional multi-target detection problem of recovering a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. Motivated by the structure reconstruction…
Although deep learning has significantly improved Face Recognition (FR), dramatic performance deterioration may occur when processing Low Resolution (LR) faces. To alleviate this, approaches based on unified feature space are proposed with…