Related papers: Algebraic compressed sensing
In this paper, we study the support recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
We consider multi-label prediction problems with large output spaces under the assumption of output sparsity -- that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting…
Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video…
The problem of recovering a structured signal $\mathbf{x} \in \mathbb{C}^p$ from a set of dimensionality-reduced linear measurements $\mathbf{b} = \mathbf {A}\mathbf {x}$ arises in a variety of applications, such as medical imaging,…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm that leverages a trained generative model to enhance the signal reconstruction performance. The generator, a…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
The $\ell^0$ minimization of compressed sensing is often relaxed to $\ell^1$, which yields easy computation using the shrinkage mapping known as soft thresholding, and can be shown to recover the original solution under certain hypotheses.…
Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…
This paper proposes a learning method to construct an efficient sensing (measurement) matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximizing the entropy…
Practical applications of compressed sensing often restrict the choice of its two main ingredients. They may (i) prescribe using particular redundant dictionaries for certain classes of signals to become sparsely represented, or (ii)…
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…
In this letter, we consider the problem of detecting a high dimensional signal based on compressed measurements with physical layer secrecy guarantees. We assume that the network operates in the presence of an eavesdropper who intends to…
We consider the extensively studied problem of $\ell_2/\ell_2$ compressed sensing. The main contribution of our work is an improvement over [Gilbert, Li, Porat and Strauss, STOC 2010] with faster decoding time and significantly smaller…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…