Study On Sparse Decomposition Of Signal And Its Application In EEG Processing

Sparsity is to measure the number of null entries in the coefficients of a signal and alarger number of null entries avails for an sparser expression of signal. In manyscientific studies, it is necessary to decompose a signal sparsely or to solve a problemsparsely. The work in this dissertation is mainly expanded from the sparsity of the signaland its application in EEG problem. The work consists of two parts, one is focused onthe sparse expression of a signal, and the other is on the utilization of sparsity into EEGprocessing and EEG inverse problem. In the first part, mainly introduced is thedecomposition of a signal in an over-complete dictionary and one newly improvedsparse decomposition algorithm. In the work related with the neuro-physiological study,we mainly proposed such work as the way to evaluate the evoked potentials in themixed over-complete dictionary with sparse decomposition, a physiology dependentsparse decomposition method for EEG denoising and two EEG source imagingalgorithms combined with the sparsity of sources. The main work is as follows:1. Newly proposed is a modified MP method named two dictionaries MP (TDMP) todecompose signal more sparsely. In the iteration procedure of the two dictionariesMP, the over-complete dictionary is classified into two separate dictionaries withthe selected and unselected atoms, and in each iteration, the algorithm wasdesigned to have more chances than the original MP to choose the atom in theselected atom dictionary as the optimal atom by the constraint of a simulatedannealing threshold function, thus the algorithm avails for a more sparsedecomposition.2. Using the BFGS optimization strategy instead of the traditional Newton method to solve the l_p norm constrained sparse decomposition problem, which is often of large scale when decomposed in an over-complete dictionary. Compared with the usually adopted Newton descendent method, the solving based on BFGS can obviously improve the decomposition efficiency with a similar decomposition results.3. Based on the characteristic of signal to be evaluated, specifically designed a new method for the separation of a desired transient evoked potential (EP) from the...