Pseudoframes For Subspaces Research Articles

The Research of Dual Quarternary Pseudoframes for Hardy Space and Applications in Engineering Materials

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering.. In this work, the notion of the quarternary generalized multiresol- ution structure (TGMS) of subspace is proposed. The characteristics of quarternary affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.

Parameterization of Masks for Tight Wavelet Frames and Multiple Pseudoframes and Applications in Mechanical Engineering

Mechanical engineering is a discipline of engineering that applies the principles of engine ering, physics and materials science for analysis, design, manufacturing, and maintenance of mecha nical systems. In this work, the construction of 4-band tight wavelet frames with symmetric proper-ties using symmetric extension and parameterization of the paraunitary matrix. The notion of an 4-band generalized multiresolution structure of subspace is proposed. The characteristics of affine pseudoframes for subspaces is investigated. The construction of a generalized multiresolution structure of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obta-ined based on such a generalized multiresolution structure and a sufficient condition for its exist-ence is presented. A constructive method for affine frames of based on a generalized multi-resolution structure is presented.

Study of Matrix Transfer Multipliers for Normalized Pseudoframe Wavelets and Applications in Material Engineering

Materials engineers design, produce and evaluate materials and their use. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace L^2(R^2) is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of L^2(R^2) is studied. The pyramid decom position scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of L^2(R^2) based on a BGMS is established.

Study of Matrix Multipliers for Normalized Frame Multi-Wavelets and Applications in Engineering Material Technology

Frame theory has been the focus of active research for twenty years, both in theory and applications. Matrix Fourier multipliers send every orthonoamal wavelet to an orthonoamal wavelet. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

Subspace Affine Dual Multiple Frames with Multi-filter Functions and a General Multiresolution Structure

Abstract Frames have become the focus of active research, both in theory and in applications. The notion of a generalized multiresolution structure of L2(R) is formulated. The definition of dual multiple frames for subspaces of L2(R) is proposed. The construction of a generalralized multiresolution structure (GMS) of Paley-Wiener subspaces of L2(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L2(R) is obtained based on such a GMS. A sufficient condition on the existence of dual multiple pseodoframes is presented by means of paraunitary vector filter bank theory.

Study of Trivariate Pseudoframes and Subspace Frames and their Applications in Solid-State Physics

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering.. In this work, the notion of the trivariate generalized multiresolut- ion structure (TGMS) of subspace is proposed. The characteristics of trivariate affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.

The Characters of Multiple Tight Multivariate Wavelet Frames and Application in Quantum Physics

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This paper is devoted to the study and construction of finitely supported tight multivariate frames of multivariate multi-wavelets. Inparticular, a necessary conditi- on for their existence is obtained to present some feasible idea for designing such MRA tight frames. The characteristics of binary multiscale pseudoframes for subspaces is investigated. The constructi- on of a GMS of Paley-Wiener subspace of is studied. A constructive method for affine multivariate frames based on such a GMS is established.

The Features of Multiscale Pseudoframes and Gabor Frames According to Bivariate Filter Functions

The advantages of wavelet analysis and their promising featu-res in various application have attracted a lot of interest and effort in re-cent years. Frame analysis has become popular much later in sampling theory, time-frequency analysis and wavelet theory. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudof-rames for subspaces is investigated. The construction of a BGMS of Paley-Wiener subspace ofis studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established. A method for designing a class of affine bivariate dual frames in bi-dimensional space is presented. The results we obtain gains much improvement.

Constructional Approaches on Vector-Valued Wavelets with Multi-Scale Dilation Factor

In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of finitely supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is investigated. A new method for construc- -ting a class of biorthogonal finitely supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory. A sufficient condition for the existence of multiple pseudoframes for subspaces is derived

The Information Fusion Method Based on a Sort of Multiple Pseudoframes with Arbitrary Real Translation Constant

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. The definition of multiple pseudofames for subspaces with real number translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The pyramid decomposition scheme is derived based on a GMS. As a major new constribution the sufficient condition for the existence of multiple pseudoframes for subspaces is derived based on such a GMS.

The Research of Multiple Subspace Pseudoframes with Integer Translation

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The construction of a GMS of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a GMS. As a major new constribution the sufficient condition for the existence of multiple pseudoframes for subspaces is derived based on such a GMS.

The Character of Multiple Affine Pseudoframes with Filter Banks Based on a Pyramid Decomposition Scheme

In recent years, frames have been the focus of active research, both in theory and applications. In this paper, the notion of multiple affine pseudoframes for subspaces of space is introduced. The concept of a generalized multiresolution structure(GMRS) is proposed. The sufficient condition for the existence of a class of multiple pseudoframes with filter banks is obtained by virtue of a generalized multiresolution structure. An approach for constructing one GMRS of Paley-Wiener subspaces of is presented based on the pyramid decomposition scheme The characteristics of affine pseudoframes for subspaces of space is provided.

The Characteristics of Affine Bivariate Pseudoframes of Subspace Associated with a Bivariate Filter Functions

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

Beurling Dimension of Gabor Pseudoframes for Affine Subspaces

Pseudoframes for subspaces have been recently introduced by Li and Ogawa as a tool to analyze lower dimensional data with arbitrary flexibility of both the analyzing and the dual sequence. In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets of parameters. We first introduce a new notion of Beurling dimension for discrete subsets of ℝ d by employing a certain generalized Beurling density. We present several properties of Beurling dimension including a comparison with other notions of dimension showing, for instance, that our notion includes the mass dimension as a special case. Then we prove that Gabor pseudoframes for affine subspaces satisfy a certain Homogeneous Approximation Property, which implies invariance under time–frequency shifts of an approximation by elements from the pseudoframe. The main result of this paper is a classification of Gabor pseudoframes for affine subspaces by means of the Beurling dimension of their sets of parameters. This provides us, in particular, with a Nyquist dimension which separates sets of parameters of pseudoframes from those of non-pseudoframes and which links a fixed value to sets of parameters of pseudo-Riesz sequences. These results are even new for the special case of Gabor frames for an affine subspace.

Optimal noise suppression: A geometric nature of pseudoframes for subspaces

Pseudoframes for subspaces (PFFS) is a notion of frame-like expansions for a subspace \(\chi\) in a separable Hilbert space [11]. The spanning nature of the sequences \(\{x_n\}\) and \(\{x^*_n\}\) in a PFFS (relative to the subspace \(\chi\)) is generally very different from that of a frame. Incidentally, a PFFS constitutes generally a nonorthogonal projections onto \(\chi\). The directions of the projection determine the geometric meanings and its applications of a PFFS. PFFS also provides a means for the construction of nonorthogonal projections that arises in various linear reconstruction problems. This article is aimed at elaborations on such geometrical properties, demonstration of natural needs of nonorthogonal projections in applications and how PFFS can be applied, particularly for optimal noise suppressions. In this specific application, we show that PFFS is not only natural and sufficient but also necessary for generating an optimal solution among the class of all linear and series-based methods.

Affine pseudoframes for subspaces of L2(R) associated with a generalized multiresolution structure

Abstract In this paper, the notion of an m -band generalized multiresolution structure (GMS) of L 2 ( R ) is introduced. We give the definition and the characterization of affine pseudoframes for subspaces. The construction of a GMS of Paley–Wiener subspaces of L 2 ( R ) is investigated. The pyramid decomposition scheme is derived based on such a GMS. As a major new contribution the construction of affine frames for L 2 ( R ) based on a GMS is presented.

Pseudoframes for Subspaces with Applications

A notion of pseudoframes for subspaces (PFFS) is defined and characterized in a separable Hilbert space H. PFFS functions in a manner of a frame for a subspace X in H. Yet none of the pair of sequences {xn} and {x*n} is necessarily contained in X. This gives rise to attractive properties that center around the flexibility. A necessary and sufficient characterization of PFFSs is provided. Analytical formulae for the constructions of PFFSs in two directions are derived. Examples are considered. Some insight relationships of an PFFS for X and a frame of X are also observed thanks to a private communication with Casazza. Further applications of PFFSs are also discussed.