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## Manni-Palumbo Bidimensional Empirical Mode Decomposition (MPBEMD)

It is a recent and innovative signal processing technique that allows to analyze non-stationary and non-linear two-dimensional data sets, decomposing a complex data set into a finite set of Intrinsic Mode Functions, also called IMFs.

## What is it

MPBEMD is an innovative **signal decomposition tecnique**: it allows you to split a signal in fundamental modes, each with its own meaning, without loss information and in the time domain (bye bye Fourier!).

The decomposition method is based on the **Empirical Mode Decomposition**(1) (**EMD**) developed by **Huang et al**. (2006) and together with **Hilbert Spectral Analysis** (**HSA**) makes up the **Hilbert-Huang Transform**(2) (**HHT**).

## How does it work

Formally, MPBEMD is a signals decomposition technique that **allows you to analyze not stationary and non-linear two-dimensional data sets**, splitting a complex data set into a finite set of **Intrinsic Mode Function***, also called IMF.*

## Intrinsic Mode Function

The IMF is a function that represents a **single oscillation mode** of the signal, ie a curve that contains a given information content into the original signal. It would be the counterpart of a **simple harmonic function**, but its definition is much more general. It can have variable frequency and amplitude in the time domain (it is a** non-stationary signal**).

The EMD allows to realize the function that identifies the IMF so these are spontaneously identified from the procedure; the MPBEMD can be parameterized to divide the signal into a specified number of IMFs, each one has a specific information content.

## Benefits

The MPBEMD is an intuitive and direct technique, based on local characteristics of the data (so the same extraction process is data driven) and can be extended to non-linear and stationary processes. At the end of the elaboration, you obtain a set of curves (IMFs) that allows you an intuitive analysis of the time-frequency signal characteristics.## Use

This technique can be used in many types of computer vision systems because it analyze images quickly. In fact, the MPBEMD has been successfully used in the following fields:

**biometric identification and recognition;****lossless compression;****pattern recognition;****feature extraction;****defects identification.**

## Improvements

Compared to EMD, MPBEMD makes the following improvements:

- it uses a matrix that corrects some inaccuracies calculation that plague the EMD;
- it gives a residue as flat as possible

it introduces an algorithm for the variation of the conditions of deduction of two-dimensional IMF (the stopping criteria) in order to refine and customize the extraction; - it uses the blockiness of images of considerable size to reduce the computation time;
- it uses an overlapping with a fixed window width;
- it makes a unidirectional raster scan.

[1] Huang N.E. et al. : The empirical mode decomposition and the Hilbert spectrum for nonlinear non-stationary time series analysis, Proc. R. Soc. London Ser. A 454, pp. 903–995, (1998).

[2] Kizhner S., Flatley T. P., Huang N.E., Blank K., Conwell E., On the Hilbert-Huang Transform Data Processing System Development, NASA (Goddard Space Flight Center), Greenbelt Road, Greenbelt MD, 20771 301 -286-7029 Darrell Smith, Orbital Sciences Corporation

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