We consider the problem of variation of spectral subspaces for linear self-adjoint operators with emphasis on the case of off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of the difference of two spectral projections associated with isolated parts of the spectrum of the perturbed and unperturbed operators ...

Indexing terms: Coding, Image processing, Fractal transforms In this letter the contractivity of existing fractal transforms for use in image compression schemes is examined. The coding process is described as nonlinear transformation in the finite dimensional euclidean vector space. We derive sufficient conditions for contractivity based on the spectral norm and the spectral radius of the tran...

6.1 Spectral Estimation Methods 6.1.1 Bartlett Method 6.2 Minimum Variance Distortionless Response Estimator 6.3 Linear Prediction Method 6.4 Maximum Entropy Method 6.5 Maximum Likelihood Method 6.6 Eigenstructure Methods 6.7 MUSIC Algorithm 6.7.1 Spectral MUSIC 6.7.2 Root-MUSIC 6.7.3 Constrained MUSIC 6.7.4 Beam Space MUSIC 6.8 Minimum Norm Method 6.9 CLOSEST Method 6.10 ESPRIT Method 6.11 Wei...

First we introduce some of the basic notations. For any vector u = (u1, . . . , up) T ∈ R, denote by |u|q the vector `q-norm defined by |u|q = (∑p k=1 |uk| )1/q for q ≥ 1 and write |u|0 = ∑p k=1 I(uk 6= 0). For any set S, denote by S its complement. For a matrix A = (ak`) ∈ Rp×p, we denote by ‖A‖2 the spectral norm, ‖A‖F the Frobenius norm, and ‖A‖1 = ∑p k,`=1 |ak`| the elementwise `1-norm. Rec...

We establish a connection between the L norm of sums of dilated functions whose jth Fourier coefficients are O(j−α) for some α ∈ (1/2, 1), and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain sharp conditions for the convergence in L and for the almost everywhere convergence of series of dilated functions.

6.1 Spectral Estimation Methods 6.1.1 Bartlett Method 6.2 Minimum Variance Distortionless Response Estimator 6.3 Linear Prediction Method 6.4 Maximum Entropy Method 6.5 Maximum Likelihood Method 6.6 Eigenstructure Methods 6.7 MUSIC Algorithm 6.7.1 Spectral MUSIC 6.7.2 Root-MUSIC 6.7.3 Constrained MUSIC 6.7.4 Beam Space MUSIC 6.8 Minimum Norm Method 6.9 CLOSEST Method 6.10 ESPRIT Method 6.11 Wei...

We present a new estimator for precision matrix in high dimensional Gaussian graphical models. At the core of the proposed estimator is a collection of node-wise linear regression with nonconvex penalty. In contrast to existing estimators for Gaussian graphical models with O(s √ log d/n) estimation error bound in terms of spectral norm, where s is the maximum degree of a graph, the proposed est...

Abstract—In this work, we exploit two assumed properties of the abundances of the observed signatures (endmembers) in order to reconstruct the abundances from hyperspectral data. Joint-sparsity is the first property of the abundances, which assumes the adjacent pixels can be expressed as different linear combinations of same materials. The second property is rank-deficiency where the number of ...

This paper considers a sparse spiked covariancematrix model in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of convergence for estimating the spiked covariance matrix under the spectral norm is established, which requires significantly different techniques from those fo...

In this work we give a non-trivial upper bound on the spectral norm of various Boolean predicates of the Diie-Hellman function. For instance, we consider every individual bit and arbitrary unbiased intervals. Combining the bound with recent results from complexity theory we can rule out the possibility that a Boolean function with a too small spectral norm can be represented by simple functions...