Module ceemdan 

Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)

CEEMDAN fixes two failure modes of EEMD:

1. Residual noise. EEMD averages each IMF independently, so noise is not fully cancelled and the reconstruction x = Σ IMFₖ + r only holds approximately. CEEMDAN injects noise at each sifting stage and defines IMFs telescopically (IMFₖ = rₖ₋₁ − rₖ), making exact reconstruction a structural property of the algorithm.
2. Inconsistent IMF counts across realizations. EEMD ensemble members can produce different numbers of IMFs, which forces zero-padding. CEEMDAN extracts a single IMF count from the stage-wise construction.

Variants

• CeemdanVariant::Improved (Colominas, Schlotthauer & Torres 2014, also known as ICEEMDAN) is the default. Each stage extracts the local-mean of rₖ₋₁ + βₖ₋₁ · Eₖ(wⁱ) and defines IMFₖ = rₖ₋₁ − rₖ. Fixes spurious modes and residual noise that the 2011 variant exhibits.
• CeemdanVariant::Standard (Torres, Colominas, Schlotthauer & Flandrin 2011) extracts the first IMF of the noise-augmented residue at each stage. Retained for comparison and reproducing legacy results.

Reproducibility

Noise vectors are drawn from a single seeded StdRng sequentially, so the byte stream of every noise realization is fixed by the seed alone. The downstream work is then parallelized: per-realization EMD decompositions of the noise (used to build Eₖ(wⁱ)) run across rayon workers, and within each stage ensemble-member contributions are computed in bounded chunks before being reduced into the accumulator in member-index order. Both the noise stream and the floating-point sum order are therefore independent of worker count, so for a fixed CEEMDAN::random_seed the IMFs are bitwise-identical across runs and across RAYON_NUM_THREADS.

References

• Torres, M. E., Colominas, M. A., Schlotthauer, G., & Flandrin, P. (2011). A complete ensemble empirical mode decomposition with adaptive noise. ICASSP 2011, 4144–4147. https://doi.org/10.1109/ICASSP.2011.5947265
• Colominas, M. A., Schlotthauer, G., & Torres, M. E. (2014). Improved complete ensemble EMD: A suitable tool for biomedical signal processing. Biomedical Signal Processing and Control, 14, 19–29. https://doi.org/10.1016/j.bspc.2014.06.009
• Wu, Z., & Huang, N. E. (2009). Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in Adaptive Data Analysis, 1(1), 1–41. https://doi.org/10.1142/S1793536909000047

Structs

CEEMDAN

Complete Ensemble EMD with Adaptive Noise.

Enums

CeemdanVariant

Which CEEMDAN formulation to use.