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 ...
We provide a condition on the number of samples in terms of the sparsity and the signal length which guarantees that a fixed sparse signal can be recovered with a random draw of the matrix using $\\\ell_1$-minimization. The constant 2 in the condition is optimal, and the proof is rathe...
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...
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 ...
() Citation Context ...n admits a Kashin’s representation of level C with V; (b) the matrix V satisfies B(0, √ M/C) ⊂ VQM . Random matrices V with i.i.d. subgaussian entries satisfy the above property with high probability =-=[16, 15, 14]-=-, which is why we ...
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 ...
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 (...
After proving that random matrices with uniform sub-Gaussian tailed independent coefficients satisfy the Tracy Widom bound, that is, their matrix operator norm remains bounded by $O(\\sqrt n )$ with overwhelming probability, we prove that a less stringent condition is that the matrix rows are ...
Sparse Transition Matrix Estimation for Sub-Gaussian Autoregressive Processes with Missing Datadoi:10.23919/acc.2018.8431255Amin JalaliRebecca WillettIEEEAdvances in Computing and Communications