<title>On empirical mode decomposition for ultraspectral sounder data compression</title>

Abstract

A method 7 combining the empirical mode decomposition (EMD) 6 and the principal component analysis (PCA) was recently proposed for lossless compression of ultraspectral sounder data. In that method, data residual is obtained via the linear regression of the data against m intrinsic mode functions (IMFs) which are obtained from the EMD of the data mean, followed by the linear regression of the IMF regression error against a truncated number, n, of the corresponding principal components (PCs). In this paper we show that this two-stage (m IMFs + n PCs) linear transform approach is not as good as its counterpart two-stage (m PCs + n PCs) linear transform approach in terms of data residual and compression ratio of ultraspectral data, given the same number of IMFs and PCs used respectively at the first stage, followed by the same number of PCs used at the second stage. Mathematically, the two-stage (m PCs + n PCs) linear transform approach is equivalent to a single linear transform with (m + n) PCs. In other words, the simple PCA compression method outperforms this combined EMD and PCA compression method. This is expected because the PCA (a.k.a. the Karhunen-Loeve transform or the Hotelling transform) is known to be the optimal linear transform in the sense of minimizing the mean squared error. Our compression experiment confirms our conjecture that the role of EMD in the EMD + PCA approach is not only redundant but also degrades the compression ratios as compared to the PCA approach. We also compare the effect of using a partial set of 1502 channels against using the full set of 2107 channels, and show that the EMD + PCA approach does not break the 3:1 lossless compression barrier when compressing the full set of 2107 channels in the standard ultraspectral test data set. Our lossless PCA approach is the first to break the 3:1 compression barrier for the full set of this class of data.