730 research outputs found
An Optimization Based Empirical Mode Decomposition Scheme for Images
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 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
A unique polar representation of the hyperanalytic signal
The hyperanalytic signal is the straight forward generalization of the
classical analytic signal. It is defined by a complexification of two canonical
complex signals, which can be considered as an inverse operation of the
Cayley-Dickson form of the quaternion. Inspired by the polar form of an
analytic signal where the real instantaneous envelope and phase can be
determined, this paper presents a novel method to generate a polar
representation of the hyperanalytic signal, in which the continuously complex
envelope and phase can be uniquely defined. Comparing to other existing
methods, the proposed polar representation does not have sign ambiguity between
the envelope and the phase, which makes the definition of the instantaneous
complex frequency possible.Comment: 2014 IEEE International Conference on Acoustics, Speech, and Signal
Processing (ICASSP
A different view on the vector-valued empirical mode decomposition (VEMD)
The empirical mode decomposition (EMD) has achieved its reputation by
providing a multi-scale time-frequency representation of nonlinear and/or
nonstationary signals. To extend this method to vector-valued signals (VvS) in
multidimensional (multi-D) space, a multivariate EMD (MEMD) has been designed
recently, which employs an ensemble projection to extract local extremum
locations (LELs) of the given VvS with respect to different projection
directions. This idea successfully overcomes the problems of locally defining
extrema of VvS. Different from the MEMD, where vector-valued envelopes (VvEs)
are interpolated based on LELs extracted from the 1-D projected signal, the
vector-valued EMD (VEMD) proposed in this paper employs a novel back projection
method to interpolate the VvEs from 1-D envelopes in the projected space.
Considering typical 4-D coordinates (3-D location and time), we show by
numerical simulations that the VEMD outperforms state-of-art methods.Comment: 7th International Congress on Image and Signal Processing (CISP
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