An Efficient Blind Source Separation Based on Adaptive Wavelet Filter and SFA

Slow Feature Analysis (SFA) for vector-valued functions of several variables and apply it to the problem of blind source separation, in particular to image separation. It is generally necessary to use multivariate SFA instead of univariate SFA for separating multi-dimensional signals. For the linear case, an exact mathematical analysis is given, which shows in particular that the sources are perfectly separated by SFA if and only if they and their first-order derivatives are uncorrelated. A new construction of nonlinear locally adaptive wavelet filter banks by connecting the lifting scheme with the idea of image smoothing. The WAF consists of two parts. The first part is a wavelet transform that decomposes into seven frequency bands. The second part is an adaptive filter that uses the signal of the seventh lowest-frequency band among the wavelet transformed signals as primary input and a constant as reference input. To evaluate the performance of the WAF, two baselines wandering elimination filters are used a commercial standard filter with a cutoff frequency of 0.5 Hz and a general adaptive filter.