Related papers: Support Recovery of Sparse Signals
This paper is concerned with jointly recovering $n$ node-variables $\left\{ x_{i}\right\}_{1\leq i\leq n}$ from a collection of pairwise difference measurements. Imagine we acquire a few observations taking the form of $x_{i}-x_{j}$; the…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…
Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…
We propose robust and efficient algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common…
Standard compressive sensing results state that to exactly recover an s sparse signal in R^p, one requires O(s. log(p)) measurements. While this bound is extremely useful in practice, often real world signals are not only sparse, but also…
In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
This article considers constrained $\ell_1$ minimization methods for the recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaussian noise. A unified and elementary treatment is given in these noise…
In this paper we consider asymptotically exact support recovery in the context of high dimensional and sparse Canonical Correlation Analysis (CCA). Our main results describe four regimes of interest based on information theoretic and…
We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known…
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…
We address the problem of recovering a sparse signal observed by a resource constrained wireless sensor network under channel fading. Sparse random matrices are exploited to reduce the communication cost in forwarding information to a…
In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
This work discusses the problem of sparse signal recovery when there is correlation among the values of non-zero entries. We examine intra-vector correlation in the context of the block sparse model and inter-vector correlation in the…
In this work, we study the problem of reconstructing a sparse signal from a limited number of linear 'incoherent' noisy measurements, when a part of its support is known. The known part of the support may be available from prior knowledge…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…