in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing in particular several characterizations of such thresholders. W...

We study the application of a library of orthonormal bases to the reduction of correlated Gaussian noise. A joint condition on the library and the noise covariance is derived which ensures that simple thresholding in an adaptively chosen basis yields an estimation error within a logarithmic factor of the ideal risk. In the model example of a wavelet packet library and stationary noise the condi...

| Segmented Image Coding (SIC) produces images of better subjective quality than techniques such as the Joint Photographic Experts Group (JPEG) standard at very low bit rates. It segments images into regions of similar texture and codes their contour and texture separately. Most SIC techniques represent the texture as a linear combination of orthonormal base functions, which diier from region t...

We study a class of orthonormal exponential bases for the space L2[0, 1] and introduce the concept of spectral sequences. We characterize piecewise linear spectral sequences with the knot at 1/2 and investigate the non-continuity of the piecewise linear spectral sequences. From a special construction of a piecewise constant spectral sequence, the classical Walsh system is recovered.

The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any f...

Orthonormal spin-flavor wave functions of Lorentz covariant quark models of the Bakamjian-Thomas type are constructed for nucleon resonances. Three different bases are presented. The manifestly Lorentz covariant Dirac-Melosh basis is related to the Pauli-Melosh basis and the symmetrized Bargmann-Wigner basis that are manifestly orthogonal.

We propose alternative discriminant measures for selecting the best basis among a large collection of orthonormal bases for classi cation purposes. A generalization of the Local Discriminant Basis Algorithm of Saito and Coifman is constructed. The success of these new methods is evaluated and compared to earlier methods in experiments.