The Application And Research Of Sparse Decomposition On Signal Denoising

The21^stcentury is a time of information technology, in which the digitized signalssuch as videos and images have gradually become the main sources of people gettinginformation, replacing those traditional analog signals. But during the digitization ofanalog signals, the original signals may be brought in some noises, due to such factorsas the transformation equipments or methods. The high power noises will lead to thedescent of the signals`quality. To be more specific, the noises will on one handinfluence people from getting information, on the other hand, they will cause somemistakes to subsequent processes.That`s why denoising has always been a hotspot insignal processing. According to different theories, researchers have proposed somedifferent denoising algorithms. However, these algorithms could not implementdenoising works in some peculiar situations, for example, the power of the noise istoo high. Unlike traditional denoising algorithms,spare decomposition theoryseparates the original signals and noises by judging if they are the sparse parts of thewhole signals, which could implement signals`denoising well, especially for thosenoises with high power.This paper first explains the theory bases of sparse decomposition, and illustrates itssuperiority in expressing complicated signals and its complexity in its algorithms bycomparing with orthogonal transformations.Meanwhile,the overcomplete dictionariesplay an important pole in denoising process by sparse decomposition, so this paperfocuses on two methods to construct overcomplete dictionaries, which arerespectively Gabor dictionary and dictionary constructed according to signals`ownstructures. And then I test the two dictionaries by carrying out some experiments.With the supports by the project supported by Jilin`s Development of Sciecne andTechnology and the project supported by the National Natural Science Foundation ofChina, this paper applies denoising in those two areas above, based on the theory ofsparse decomposition. My primary studies are put on sparse decomposition`sapplication in signals`denoising.Finally I discuss its denoising effects and themethods of constructing overcomplete dictionaries.In the area of biometric identification technology, finger-veins have become a widely selected biometric feature because of its exclusiveness and invulnerability.However,during collecting the images of finger-veins, the noises are brought in due to suchfactors as equipments and methods, which will cause troubles for subsequentsegmentation and recognition. This paper, after researching on finger-veins`structurefeatures, designs a corresponding overcomplete dictionary and proposes a algorithmto denoise the images of finger-veins, based on spare decomposition. The experimentsresults indicate that this algorithm is able to pick atoms which have a similar featurewith finger-veins from the dictionary, and is able to suppress the noises well. Theexperiments also prove sparse decomposition’s ability in denoising the images offinger-veins and the correctness of the chosen dictionary.As the main ingredient of semiconductor lasers`noises in low frequency, the1/f noisesignal has a close relationship with the reliability of semiconductor lasers. The powerof1/f noise signal is so weak that it is commonly buried in white noises broughtduring collecting process, due to which the traditional denoising algorithms are unableto reach a satisfactory result. This paper, considering that the power spectral density of1/f noise signal is in the inverse ratio of frequency, designs a corresponding dictionaryand proposes a new method to estimate1/f noise’s parameter based on sparedecomposition. The experiments results indicate that this algorithm is able to pickatoms with the same frequency of1/f noise signals from the dictionary, and is able toextract the1/f noise from white noise. The estimated parameter has a good coherencewith the result detected by spectroanalyzer, which proves spare decomposition’sability in suppressing high power noises. At the same time, the correctness of thechosen dictionary is illustrated by opposite experiments.