Study On Nonlinear Blind Source Extraction And Its Applications

Blind source separation (BSS) is a signal processing method which aims atrecovering the original sources simultaneously from all kinds of their observed mixtures,without the need for prior knowledge of the mixing process and the sources themselves.It has become an important research topic in the signal processing area due to its wideapplications in many fields, such as biomedical engineering, sonar, radar, speechenhancement, telecommunications, and image processing, and so on. Most existing BSSalgorithms have been specially designed for the linear instantaneous mixture model andrecovered all the unknown sources simultaneously. In many practical situations, it ismore appropriate to model many practical problems to the nonlinear mixtures due to thenonlinear distortions that sensors introduce. Besides, only a single source or a subset ofsources is subject of interest and separating all the sources at a time could take a largetime and have mach unnecessary computation. For the above problems, in this thesis thenonlinear blind source extraction (BSE) and its applications in the biomedicalengineering are focused on and the innovative results are obtained as follows:1. A kurtosis-based nonlinear blind source extraction algorithm is proposed. Inthis algorithm, the prior knowledge of the normalized kurtosis range about the desiredsource is treated as a constraint and incorporated into the contrast function of blindsource separation. Therefore, a constrained optimization problem is formulated. By theaugmented Lagrange function method, this constrained optimization problem istransformed into an unconstrained optimization problem, which is solved by thestandard gradient descent learning. Due to the use of the prior knowledge, the source ofinterest can be extracted at a time from the post-nonlinear (PNL) mixtures by thisalgorithm, which effectively avoids much unnecessary calculations and saves a lot oftime.2. A reference-based nonlinear blind source extraction algorithm is proposed.First, the traditional constrained independent component analysis (cICA) framework isextended to the PNL mixture model. Then, a reference-based nonlinear blind sourceextraction algorithm is proposed based on this new framework. In this algorithm, thecloseness measure between the estimated output and the reference signal is treated as a new objective function. By alternately optimizing the contrast function and this newobjective function with standard gradient ascent learning, the desired source can beextracted from the PNL mixtures. Due to the prior knowledge of the reference signaland circumventing the threshold per-determined problem, the computation time isreduced greatly and the accuracy of the desired source is improved.3. A Gaussianization-based nonlinear blind source extraction algorithm isproposed. The proposed algorithm is a two-stage process that consists of aGaussianizing transformation and extracting the desired source with specific kurtosisrange. First, according to the central limit theorem, the nonlinear distortions in the PNLmixture are compensated by the Gaussianizing transformation and the approximatelylinear-mixed signals are obtained. Then, with the augmented Lagrange function method,the source of interest is extracted from these signals by using the prior knowledge of thenormalized kurtosis range about the desired source. Due to two stages and avoiding theapproximation problem of the unknown functions, this algorithm is simple and flexible.Besides, the efficiency of blind source extraction is improved greatly.4. Two nonlinear fetal electrocardiogram (FECG) extraction algorithms areproposed. The extraction of FECG is an important research topic in the field of thebiomedical engineering and it has clinical significance. Based on the informationminimization principle, a new objective function is proposed. Then, based on this newobjective function, two novel algorithms to extract FECG from the nonlinear mixturesare proposed. The first one is relatively simple, in which the probability density function(PDF) is directly estimated and calculated. By the good nature of mutual informationthat it can't be affected by the invertible transformation, the PDF estimation problem iscircumvented in the second algorithm. The correctness and validity of these twoalgorithms are confirmed by the computer simulations and experiments.