Research On Signal Sparse Separation Approaches And Applications

The signal's sparse separation model and its applications have received broad attention and researchin recent years.On the one hand,a suitable signal separation model can greatly improve the signal analyzing problem by decomposinga complex signal into several simple sub-component signals.On the contrary,an unfitted separation algorithm may complicate the original problem.Therefore,for a specific application,how to find an optimal signal separation model,and further,how to improve the separation algorithm,are the key questions for application researches.In this dissertation,we focus on the signal sparse separation algorithms and its applications in physiological signal(i.e.Electrocardiograph(ECG)andPlethysmograph(PLETH))analysis and fast physiological image super-resolution reconstruction.To begin with,in the application of ECG signal enhancement,we propose asparse representation based ECG signal denoising and baselinewandering(BW)correction algorithm.Unlike the traditionalfiltering-based methods,like Fourier orWavelet transform,whichuse fixed basis,the proposed algorithm models the ECG signalas superposition of few inner structures plus additive randomnoise,where these structures(referred to here as atoms)can be learned from the input signal or a training set.Using these atoms andtheir statistical properties,we can accurately choose suitable atoms to approximate the original ECG signal andremove the noise and other artifacts such as baseline wandering.And then,based on the result of enhanced ECG signal,we propose an automatic QRS complex detection algorithm using sparse representation.Since the atoms in the learnt dictionary can also reflect the structure of QRS complex in the ECG signals,we compute the kurtosis value of them and choose atoms with large kurtosis values from the dictionary.These atoms then be modified and used as an indication function to detect and locate the QRS complexes in the enhancedECG signals.However,for real-life long time ECG monitoring,ECG signals sometimes may be submerged under some strong noise artifacts(e.g.sensor fault,strong physical movement,etc.)completely,which will lead to unaccurate QRS detection.Thus,we further propose a robust heartbeat detection using both ECG and PLETH signals.Firstly,we use ensemble empirical mode decomposition(EEMD)to enhance PLETH signals and detect each wave peaks from the enhanced signals.Then,confidenc indices of ECG and PLETH have been proposed respectively.Finally,the detection results of heartbeats are derivedby melding the detection results and their confidence indices from both ECG and PLETH signals.At last,we propose a fast single image super resolutionreconstruction(SRR)approach via image sparse separation.Based on the assumption that theedges,corners,and textures in the image have different mathematical models,we apply different image SRR algorithmsto process them individually.Thus,our approachis divided into three steps:1)separating the given imageinto cartoon and texture subcomponent by nonlinear filterbased image decomposition technique;2)using nonlocal self similarity model based algorithm to interpolatethe cartoon subcomponent;and using wavelet domain HiddenMarkovian Tree(HMT)model based algorithm to zoomthe texture subcomponent;and 3)fusing the interpolatedcartoon and texture subcomponents together to derive therecovered high-resolution images.Since the decompositionand super resolution algorithms in the proposed approachare mainly based on simple convolution and linear algebracomputations,it is about 10 times faster than the traditional sparse-representation based SR algorithm.To demonstrate the performance of those proposed approaches,we compare our algorithms with some other respective state-of-art approaches on several signals and images,including simulated and real-life examples.The test data set includes MIT-BIH and MIMIC-II Matched Set from PhysioNet database.The numericalresults indicate that the algorithms proposed in this thesis have respective advantages,such as efficacy,accuracy,robustness,etc.This thesis explores a reasonableway to research signal and image separationapproaches and also their applications in the physiological signal analysis and image processing.