Equivalent Effect Function and Fast Intrinsic Mode Decomposition

TL;DR

This paper introduces the Equivalent Effect Function (EEF), a novel method for intrinsic mode decomposition and data fitting, applicable to 1D time series and 2D images, with demonstrated applications on stock data and images.

Contribution

The paper proposes a new EEF-based approach for fast intrinsic mode decomposition and extends it to 2D, addressing inter slice non-continuity issues.

Findings

Effective extraction of trend and fluctuation components from stock data.

Successful 2D image decomposition demonstrating the method's versatility.

Improved continuity in 2D intrinsic mode decomposition.

Abstract

The Equivalent Effect Function (EEF) is defined as having the identical integral values on the control points of the original time series data; the EEF can be obtained from the derivative of the spline function passing through the integral values on the control points. By choosing control points with different criteria, the EEF can be used to find the intrinsic mode function(IMF, fluctuation) and the residue (trend); to fit the curve of the original data function; and to take samples on original data with equivalent effect. As examples of application, results of trend and fluctuation on real stock historical data are calculated on different time scales. A new approach to extend the EEF to 2D intrinsic mode decomposition is introduced to resolve the inter slice non continuity problem, some photo image decomposition examples are presented.