Optimal Basis from Empirical Orthogonal Functions and Wavelet Analysis for Data Assimilation: Optimal Basis WADAi
نویسندگان
چکیده
Wavelet Analysis provides a new orthogonal basis set which is localized in both physical space and Fourier transform space. Empirical Orthogonal Functions (EOFs), on the other hand, provide a global representation of data sets. Here we investigate the various ways in which one can combine these basis sets for optimal representation of data. EOFs represent the global large scale information and wavelet analysis are used to supplement this large scale information with local fine scale information. Here we begin to explore the application of these two basis sets for outputs from an Ocean General Circulation Model and we explore various applications, including data assimilation.
منابع مشابه
Optimal Wavelet Basis for Image Compression
Unlike Fourier basis which constitutes fixed sine and cosine waves; the Wavelet Transform has infinite basis functions. The choice of good basis is application dependent. Statistical parameters of the image are dynamic and differ from image to image. A moment vector of natural image will be different from the moment vector of synthetic image. Similarly the edges in natural image have structural...
متن کاملUnconditional Bases are Optimal Bases for Data Compression and for Statistical Estimation
An orthogonal basis of L which is also an unconditional basis of a functional space F is a kind of optimal basis for compressing, estimating, and recovering functions in F . Simple thresholding operations, applied in the unconditional basis, work essentially better for compressing, estimating, and recovering than they do in any other orthogonal basis. In fact, simple thresholding in an uncondit...
متن کاملA Numerical Approach for Fractional Optimal Control Problems by Using Ritz Approximation
In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the num...
متن کاملA meshless method for optimal control problem of Volterra-Fredholm integral equations using multiquadratic radial basis functions
In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...
متن کاملFresnelets: new multiresolution wavelet bases for digital holography
We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of L2 to which we apply a unitary Fresnel transform. The transformed basis functions are shift-invariant on a level-by-level basis but their multiresolution properties are governed by...
متن کامل