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Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
We consider the problem of robustly recovering a $k$-sparse coefficient vector from the Fourier series that it generates, restricted to the interval $[- \Omega, \Omega]$. The difficulty of this problem is linked to the superresolution…
Spatial mode demultiplexing was proved to be a successful tool for estimation of the separation between incoherent sources, allowing for sensitivity much below the Rayleigh limit. However, with the presence of measurement's noise,…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper…
We address the problem of super-resolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks.…
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…
We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…
Image super-resolution (SR) is one of the long-standing and active topics in image processing community. A large body of works for image super resolution formulate the problem with Bayesian modeling techniques and then obtain its…
In this work we demonstrate the use of neural networks for rapid extraction of signal parameters of discretely sampled signals. In particular, we use dense autoencoder networks to extract the parameters of interest from exponentially…
In large-scale spatial surveys, such as the forthcoming ESA Euclid mission, images may be undersampled due to the optical sensors sizes. Therefore, one may consider using a super-resolution (SR) method to recover aliased frequencies, prior…
Super-resolution (SR) aims to increase the resolution of imagery. Applications include security, medical imaging, and object recognition. We propose a deep learning-based SR system that takes a hexagonally sampled low-resolution image as an…
Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…
Super-resolution (SR) has traditionally been based on pairs of high-resolution images (HR) and their low-resolution (LR) counterparts obtained artificially with bicubic downsampling. However, in real-world SR, there is a large variety of…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
We address the problem of super-resolution of point sources from binary measurements, where random projections of the blurred measurement of the actual signal are encoded using only the sign information. The threshold used for binary…