Related papers: Super-Resolution of Point Sources via Convex Progr…
We consider imaging of two partially coherent sources and derive the ultimate quantum limits for estimating the separation, location, relative intensity, and coherence factor. We show that super-resolution in the separation is achievable…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
In many applications we seek to recover signals from linear measurements far fewer than the ambient dimension, given the signals have exploitable structures such as sparse vectors or low rank matrices. In this paper we work in a general…
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…
The theory of compressive sensing (CS) suggests that under certain conditions, a sparse signal can be recovered from a small number of linear incoherent measurements. An effective class of reconstruction algorithms involve solving a convex…
We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…
In this paper, we investigate the recovery of the sparse representation of data in general infinite-dimensional optimization problems regularized by convex functionals. We show that it is possible to define a suitable non-degeneracy…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
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…
We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…
Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
In the practical applications of computed tomography imaging, the projection data may be acquired within a limited-angle range and corrupted by noises due to the limitation of scanning conditions. The noisy incomplete projection data…
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…
This paper discusses the recovery of an unknown signal $x\in \mathbb{R}^L$ through the result of its convolution with an unknown filter $h \in \mathbb{R}^L$. This problem, also known as blind deconvolution, has been studied extensively by…
This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm…
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…
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…