Wavelet and principal component subspace analysis for function approximation and data compression

A method for a wavelet analysis of time series or image data is presented in which correlation among the data component is used to increase the efficiency of function approximation and data compression. For this purpose, the sub-space analysis of the principal components is utilized. Wavelet coefficients belonging to the first component are derived and stored for function reconstruction. A residual of the data is reconstructed for a recursive implementation of the algorithm. The proposed method allows the use different wavelet function at each stage, for a hierarchically efficient decomposition of the signal data. A thresholding of the principal components, eliminates the entry of coefficients of small magnitude to later stages and improves the efficiency of the algorithm. A formal approach for a best basis selection within the context of the principal component analysis and ellipsoidal signal model using Kolmogorov n-width concept is also given.