Research On Denoising Methods Of Signals Based On Sparse Decomposition

Signal denoising is a classical basic subject of the signal processing field.Denoising method based on sparse decomposition in the redundancy dictionaryimplements the more concise and comprehensive sparse representations toeventually effective separate useful signal and noise signal, which is concerned bymany researchers. Sparse decomposition was widely used in signal denoising suchas speech signal, image signals, medical signal, earthquake, radar signal and theultrasonic signals, and many other signals.The sparse decomposition denoisingmethods are discussed in this dissertation. Aimed to improve signal denoisingperformance and reducing the complexity, this paper studys the denoising methodsbased on some sparse characteristics of special signals such as block-sparse signals,tree-sparse signal and multichannel signal which with signal correlation. Simulationresults on synthetic signal and real signal verify the superiority and effectiveness ofthe algorithms described in this thesis.The main research contents and research results of the thesis are as follows:1．Sparse decomposition denoising theory and its main denoising algorithmsare studied. First of all, the sparse decomposition basic model and the mathematicaldescription of the sparse decomposition denoising are discussed. Then thedenoising algorithms are researched, and simulation results show that sparsedecomposition denoising methods has obvious advantages compared with theorthogonal decomposition and wavelet threshold.2．Sparse decomposition denoising algorithms based on signal model arestudied. Focous on the problems that the existing sparse decomposition denoisingalgorithms did not take into account the issue of signal sparse characteristic, thisdissertation proposes sparse decomposition matching pursuit denoising methodsface to block-sparse signal and tree-sparse signal, respectively. Firstly, turning thecluster structure characteristics of the block-sparse signals into the matching pursuitdenoising methods, a class of block-sprase matching pursuit sparse decompositionalgorithms which can improve the matching speed and accuracy has been proposed.The simulation experiments verify the effectiveness of the proposed algorithm, isshown as the computing complexity and denoising effect is superior to existingmatching pursuit sparse decomposition denoising algorithm. Subsequently, based on the characteristic of the largest coeffcients cluster along the branches of this treeof greedy wavelet tree and optimal wavelet tree, a class of tree-sprase matchingpursuit sparse decomposition algorithms has been proposed. Simulationexperiments show the proposed algorithm has favourable denoising performanceboth on greedy wavelet tree and optimal wavelet tree signals.3. Multichannel signal sparse decomposition denoising algorithms based onsignal correlation are studied. To solve the problem that sparse decompositiondenoising filed without involving the multichannel signal joint denoising, twocorrelation models(CMs) are established combination with the practicalmultichannel application scenarios. Then according to the two CMs, newmultichannel matching pursuit sparse decomposition denoising algorithms arestudied respectively. Firstly, due to the CM1model signals have the public sparsepart, decomposing single signal to gain public parts as prior knowledge to getspecific part of the other signal, a class of CM1denoising algorithms are proposed.The simulation results show that the proposed algorithm in terms of denoisingeffect and computational complexity are improved. In addition, according to thecharacteristics of CM2model signals with the same sparse base and combined tomultichannel signal set, a class of CM2denoising algorithms which improved theatom matching accuracy are proposed. Simulation experiments on synthetic signaland real signal verify the effectiveness of the proposed algorithm.