Related papers: Compressed sensing with corrupted Fourier measurem…
Consider the problem of reconstructing a multidimensional signal from an underdetermined set of measurements, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such…
One-bit compressed sensing (1bCS) addresses the recovery of sparse signals from highly quantized measurements, retaining only the sign of each linear measurement. In the support recovery setting, the goal is to identify $\text{supp}(x)$,…
Radio interferometry has always faced the problem of incomplete sampling of the Fourier plane. A possible remedy can be found in the promising new theory of compressed sensing (CS), which allows for the accurate recovery of sparse signals…
The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems had been traditionally addressed within the context of sensor array signal…
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…
The l1-norm minimization problem plays an important role in the compressed sensing (CS) theory. We present in this letter an algorithm for solving the problem of l1-norm minimization for quaternion signals by converting it to second-order…
We study the problem of low-rank tensor factorization in the presence of missing data. We ask the following question: how many sampled entries do we need, to efficiently and exactly reconstruct a tensor with a low-rank orthogonal…
Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclear Magnetic Resonance (NMR), radio interferometry, helium atom scattering etc., the theory of compressed sensing with Fourier transform measurements has reached a mature…
This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…
We consider the problem of recovering a function over the space of permutations (or, the symmetric group) over $n$ elements from given partial information; the partial information we consider is related to the group theoretic Fourier…
We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
In previous work two of the authors have shown that a vector $x \in \mathbb{R}^n$ with at most $k < n$ nonzeros can be recovered from an expander sketch $Ax$ in $\mathcal{O}(\mathrm{nnz}(A)\log k)$ operations via the Parallel-$\ell_0$…
This paper studies quantized corrupted sensing where the measurements are contaminated by unknown corruption and then quantized by a dithered uniform quantizer. We establish uniform guarantees for Lasso that ensure the accurate recovery of…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
In this paper, we consider the problem of compressive sensing (CS) recovery with a prior support and the prior support quality information available. Different from classical works which exploit prior support blindly, we shall propose novel…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent…