Related papers: Blind Recovery of Sparse Signals from Subsampled C…
Let $x\in\mathbb{C}^n$ be a spectrally sparse signal consisting of $r$ complex sinusoids with or without damping. We consider the spectral compressed sensing problem, which is about reconstructing $x$ from its partial revealed entries. By…
Blind image deblurring is the process of recovering a sharp image from a blurred one without prior knowledge about the blur kernel. It is a small data problem, since the key challenge lies in estimating the unknown degrees of blur from a…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
This paper proposes a novel approach to regularize the ill-posed blind image deconvolution (blind image deblurring) problem using deep generative networks. We employ two separate deep generative models - one trained to produce sharp images…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
The theory of Compressed Sensing (CS) asserts that an unknown signal $x\in\mathbb{R}^p$ can be accurately recovered from an underdetermined set of $n$ linear measurements with $n\ll p$, provided that $x$ is sufficiently sparse. However, in…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
Retinal implants aim to restore functional vision despite photoreceptor degeneration, yet are fundamentally constrained by low resolution electrode arrays and patient-specific perceptual distortions. Most deployed encoders rely on…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
In this paper, we present an approach to the reconstruction of signals exhibiting sparsity in a transformation domain, having some heavily disturbed samples. This sparsity-driven signal recovery exploits a carefully suited random sampling…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus.…
The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smooth \ell_1/\ell_2 regularization term. As the mean…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding…
We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is…
Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…