An Optimization Based Empirical Mode Decomposition Scheme for Images

Huang, Boqiang and Kunoth, Angela (2012) An Optimization Based Empirical Mode Decomposition Scheme for Images. (Submitted)

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Bidimensional empirical mode decompositions (BEMD) have been developed to decompose any bivariate function or image additively into multiscale components, so-called intrinsic mode functions (IMFs), which are approximately orthogonal to each other with respect to the $\ell_2$ inner product. In this paper, a novel optimization problem is designed to achieve this decomposition which takes into account important features desired of the BEMD. Specifically, we propose a data-adapted iterative method which we call Opt-BEMD which minimizes in each iteration a smoothness functional subject to inequality constraints involving the strictly local extrema of the image. In this way, the method constructs a sparse data-adapted basis for the input function as well as an envelope in a mathematically stringent sense. Moreover, we propose an ensemble version of Opt-BEMD to strengthen its performance when applied to noise-contaminated images or images with only few extrema.

Item Type: Article
Depositing User: Prof. Dr. Angela Kunoth
Date Deposited: 31 Oct 2012 11:59
Last Modified: 18 Apr 2018 01:46

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