AFD Types Sparse Representations vs. the Karhunen-Loeve Expansion for Decomposing Stochastic Processes

  title={AFD Types Sparse Representations vs. the Karhunen-Loeve Expansion for Decomposing Stochastic Processes},
  author={Tao Qian and Wei Qu},
A BSTRACT . This article introduces adaptive Fourier decomposition (AFD) type methods, emphasizing on those that can be applied to stochastic processes and random fields, mainly including stochastic adaptive Fourier decomposition and stochastic pre-orthogonal adaptive Fourier decomposition. We establish their algorithms based on the covariant function and prove that they enjoy the same convergence rate as the Karhunen-Lo`eve (KL) decomposition. The AFD type methods are compared with the KL… 

Figures and Tables from this paper

Sampling Gaussian Stationary Random Fields: A Stochastic Realization Approach

This paper proposes an efficient stochastic realization approach for sampling Gaussian stationary random fields from a systems and control point of view and shows that this approach performs favorably compared with covariance matrix decomposition methods.



A Sparse Representation of Random Signals

The purpose of the present study is to generalize both AFD and POAFD to random signals and develop an AFD type sparse representation for one-dimensional random signals by making use analysis of one complex variable.

An Introduction to Computational Stochastic PDEs

This book offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis and theory is developed in tandem with state-of-the art computational methods through worked examples, exercises, theorems and proofs.

Sparse Representation of Approximation to Identity

Best kernel approximation in Bergman spaces

A stochastic sparse representation: n-best approximation to random signals and computation

Orthogonalization in Clifford Hilbert modules and applications

We prove that the Gram–Schmidt orthogonalization process can be carried out in Hilbert modules over Clifford algebras, in spite of the uninvertibility and the un-commutativity of general Clifford

The Karhunen-Loève Theorem

    The univariate Karhunen-Loève Expansion is the decomposition of a continuous-parameter second-order stochastic process into uncorrelated random coe cients. In the present dissertation, the expansion

    A Theory on Non-Constant Frequency Decompositions and Applications

    Positive time-varying frequency representation of transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two

    Reproducing Kernel Sparse Representations in Relation to Operator Equations

    A linear operator in a Hilbert space defined through inner product against a kernel function naturally introduces a reproducing kernel Hilbert space structure over the range space. Such formulation,