Related papers: Denoising guarantees for optimized sampling scheme…

Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…

In compressed sensing the goal is to recover a signal from as few as possible noisy, linear measurements. The general assumption is that the signal has only a few non-zero entries. The recovery can be performed by multiple different…

We proposed a weighted l1 minimization to recover a sparse signal vector and the corrupted noise vector from a linear measurement when the sensing matrix A is an m by n row i.i.d subgaussian matrix. We obtain both uniform and nonuniform…

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…

Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…

Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct low-dimensional…

Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition…

In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem…

The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…

Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal,…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…

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 improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has…

Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples…

Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…

We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements…