Related papers: Rigorous Restricted Isometry Property of Low-Dimen…
The purpose of this paper is twofold. The first is to point out that the Restricted Isometry Property (RIP) does not hold in many applications where compressed sensing is successfully used. This includes fields like Magnetic Resonance…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
The Restricted Isometry Property (RIP) is a fundamental property of a matrix which enables sparse recovery. Informally, an $m \times n$ matrix satisfies RIP of order $k$ for the $\ell_p$ norm, if $\|Ax\|_p \approx \|x\|_p$ for every vector…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning. RIP matrices with optimal parameters are mainly obtained via probabilistic arguments, as explicit…
This paper discusses reconstruction of signals from few measurements in the situation that signals are sparse or approximately sparse in terms of a general frame via the $l_q$-analysis optimization with $0<q\leq 1$. We first introduce a…
We formulate a generalization of the Restricted Isometry Property (RIP) referred to as the Restricted Quasiconvexity Isometry Property (RQIP) for alpha stable random projections with $0<\alpha<1$. A lower bound on the number of rows for…
The Restricted Isometry Property (RIP) introduced by Cand\'es and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal,…
Restricted isometry property (RIP), essentially stating that the linear measurements are approximately norm-preserving, plays a crucial role in studying low-rank matrix recovery problem. However, RIP fails in the robust setting, when a…
Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are…
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…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…
We provide a simple proof of the Johnson-Lindenstrauss lemma for sub-Gaussian variables. We extend the analysis to identify how sparse projections can be, and what the cost of sparsity is on the target dimension.The Johnson-Lindenstrauss…
In compressed sensing, the restricted isometry property (RIP) on $M \times N$ sensing matrices (where $M < N$) guarantees efficient reconstruction of sparse vectors. A matrix has the $(s,\delta)$-$\mathsf{RIP}$ property if behaves as a…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
In previous work, theoretical analysis based on the tensor Restricted Isometry Property (t-RIP) established the robust recovery guarantees of a low-tubal-rank tensor. The obtained sufficient conditions depend strongly on the assumption that…
We consider the problem of constructing a linear map from a Hilbert space $\mathcal{H}$ (possibly infinite dimensional) to $\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\mathcal{S} \subset…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
The multilabel learning problem with large number of labels, features, and data-points has generated a tremendous interest recently. A recurring theme of these problems is that only a few labels are active in any given datapoint as compared…
The Johnson-Lindenstrauss (JL) theorem states that a set of points in high-dimensional space can be embedded into a lower-dimensional space while approximately preserving pairwise distances with high probability Johnson and Lindenstrauss…