We study when a sub‐Gaussian matrix can become a near isometry on a set, show that previous best‐known dependence on the sub‐Gaussian norm was suboptimal, and present the optimal dependence. Our result not only answers a remaining question posed by Liaw, Mehrabian, Plan, and Vershynin ...
Random matrices have become a popular choice for the measurement matrix. Indeed, near-optimal uniform recovery results have been shown for such matrices. In this note we focus on nonuniform recovery using Gaussian random matrices and $\\\ell_1$-minimization. We provide a condition on the number...
In this paper,sub-Gaussian random projection is introduced into compressed sensing(CS) theory and two new kinds of CS measurement matrix:sparse projection matrix and very sparse projection matrix are presented. 将亚高斯随机投影引入可压缩传感CS(compressed sensing)理论,给出了两种新类型的CS测量矩阵:稀...
The second type of sparsity in a quadratic form comes from the setting where we randomly sample the elements of an anisotropic subgaussian vector Y = H X Y = H X where H \\in \\mathbb{R}^{mimes m} H \\in \\mathbb{R}^{mimes m} is an m imes m m imes m symmetric matrix; ...
This scheme is a new algorithm for obtaining the best user ordering and channel-input covariance matrix that maximizes the total channel throughput. The proposed algorithm has linear complexity in the number of multi-carrier frequencies. The simplicity of a linear transmitter-and-receiver architecture ...
Matrix-valued wavelet series expansions for wide-sense stationary processes are studied in this paper. The expansion coefficients a are uncorrelated matrix... Z Ping,G Liu,C Zhao - 《IEEE Transactions on Signal Processing》 被引量: 23发表: 2004年 Stochastic expansions in an overcomplete wavelet ...
tail boundsub-Gaussian matrixIn this paper,we obtain a refined non-asymptotic tail bound for the largest singular value(the soft edge)of sub-Gaussian matrix.As an application,we use the obtained theorem to compute the tail bound of the Gaussian Toeplitz matrix.Xianjie GAOChao ZHANGHongwei ZHANG...
We present a simple solution to a question posed by Candes, Romberg and Tao\non the uniform uncertainty principle for Bernoulli random matrices. More\nprecisely, we show that a rectangular k*n random subgaussian matrix (with k <\nn) has the property that by arbitrarily extracting any m (...
In this direction, we show that as a matrix D stays bounded away from zero in norm on a set S and a provided map 桅 comprised of i.i.d. subgaussian rows has number of measurements at least proportional to the square of w(DS), the Gaussian width of the related set DS, then with...
In this paper,sub-Gaussian random projection is introduced into compressed sensing(CS) theory and two new kinds of CS measurement matrix:sparse projection matrix and very sparse projection matrix are presented. 将亚高斯随机投影引入可压缩传感CS(compressed sensing)理论,给出了两种新类型的CS测量矩阵:稀...