Related papers: A conditional construction of restricted isometrie…
The restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and…
We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…
The Fourier restriction problem asks when it is meaningful to restrict the Fourier transform of a function to a given set. Many of the key examples are smooth co-dimension 1 manifolds, although there is increasing interest in fractal sets.…
While most existing sparse recovery results allow only minimal structure within the measurement scheme, many practical problems possess significant structure. To address this gap, we present a framework for structured measurements that are…
Let $V$ be a vector space endowed with a non-degenerate quadratic form $Q$. If the base field $\mathbb{F}$ is different from $\mathbb{F}_2$, it is known that every isometry can be written as a product of reflections. In this article, we…
We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.
A signal is sparse in one of its representation domain if the number of nonzero coefficients in that domain is much smaller than the total number of coefficients. Sparse signals can be reconstructed from a very reduced set of…
The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix $C$ into a product $X Y$, where the factors $X$ and $Y$ are…
Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern important properties of the measured sparse signal. Of…
In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted…
In this paper, we prove that the Paley graph conjecture implies that the Paley matrix has restricted isometry property (RIP) beating the square-root bottleneck for the sparsity level. Moreover, we show that the RIP of the Paley matrix…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
In compressed sensing, the "restricted isometry property" (RIP) is a sufficient condition for the efficient reconstruction of a nearly k-sparse vector x in C^d from m linear measurements Phi x. It is desirable for m to be small, and for Phi…
We construct a basis of sparse eigenvectors for the N-dimensional discrete Fourier transform. The sparsity differs from the optimal by at most a factor of four. When N is a perfect square, the basis is orthogonal.
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…
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…
We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization…