相关论文: Revisiting RIP guarantees for sketching operators …
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…
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)…
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…
Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the…
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…
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…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
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…
Compressed sensing is a celebrated framework in signal processing and has many practical applications. One of challenging problems in compressed sensing is to construct deterministic matrices having restricted isometry property (RIP). So…
Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthogonal design matrices, and can be upper bounded in function…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…
This paper describes a coded aperture and keyed exposure approach to compressive video measurement which admits a small physical platform, high photon efficiency, high temporal resolution, and fast reconstruction algorithms. The proposed…
Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive recursion (PR) is a fast, recursive algorithm for…
A matrix $A \in \mathbb{C}^{q \times N}$ satisfies the restricted isometry property of order $k$ with constant $\varepsilon$ if it preserves the $\ell_2$ norm of all $k$-sparse vectors up to a factor of $1\pm \varepsilon$. We prove that a…
The restricted isometry property (RIP) is an important matrix condition in compressed sensing, but the best matrix constructions to date use randomness. This paper leverages pseudorandom properties of the Legendre symbol to reduce the…
Dimensionality reduction is a popular approach to tackle high-dimensional data with low-dimensional nature. Subspace Restricted Isometry Property, a newly-proposed concept, has proved to be a useful tool in analyzing the effect of…
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets,…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…
In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search…