Related papers: Derandomizing restricted isometries via the Legend…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
When the linear measurements of an instance of low-rank matrix recovery satisfy a restricted isometry property (RIP)---i.e. they are approximately norm-preserving---the problem is known to contain no spurious local minima, so exact recovery…
Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…
We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be…
Although good encryption functions are probabilistic, most symbolic models do not capture this aspect explicitly. A typical solution, recently used to prove the soundness of such models with respect to computational ones, is to explicitly…
Recovery of the initial state of a high-dimensional system can require a large number of measurements. In this paper, we explain how this burden can be significantly reduced when randomized measurement operators are employed. Our work…
We make a trivial modification to the elegant analysis of Garg and Khandekar (\emph{Gradient Descent with Sparsification} ICML 2009) that replaces the standard Restricted Isometry Property (RIP), with another RIP-type property (which could…
Sparse shrunk additive models and sparse random feature models have been developed separately as methods to learn low-order functions, where there are few interactions between variables, but neither offers computational efficiency. On the…
The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial differential equations (SPDEs). We find that if a spectral gap…
We obtain mproved bounds for one bit sensing. For instance, let $ K_s$ denote the set of $ s$-sparse unit vectors in the sphere $ \mathbb S ^{n}$ in dimension $ n+1$ with sparsity parameter $ 0 < s < n+1$ and assume that $ 0 < \delta < 1$.…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
In this paper we formulate and prove a statistical version of the Candes-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a disjoint union of orthonormal bases. In addition, we…
We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using $\ell_1$ minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
The restricted isometry property (RIP) is a universal tool for data recovery. We explore the implication of the RIP in the framework of generalized sparsity and group measurements introduced in the Part I paper. It turns out that for a…
In electrical impedance tomography, algorithms based on minimizing the linearized-data-fit residuum have been widely used due to their real-time implementation and satisfactory reconstructed images. However, the resulting images usually…
Group-sparsity is a common low-complexity signal model with widespread application across various domains of science and engineering. The recovery of such signal ensembles from compressive measurements has been extensively studied in the…
Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…