A New Sinusoidal Dictionary Modeling Of Compressed Sensing Measurements Based On Orthogonal Matching Pursuit Method

In this era of big data, the amount and speeds of information processing and transmission growsrapidly. During the digital processing times, the sampling rate limit of the classic Nyqusit theoryhas severely restricted the processing of wideband signal. It brings pressure to the data samplingequipment, besides, the further processing such as coding, also wastes storage and computingresources. Therefore, Compressed Sensing (CS) technology has been a hot research spot themoment it was born, with a much lower sampling rate than that of Nyqusit, it can sense and sampledata simultaneously. This thesis applies CS technology to the processing of speech signal. However,the first compression ratio of CS technology is much lower than the ideal one in practical use. Inorder to further compress data, the thesis analyses the characteristic of the CS measurements andputs forward a model of them.The successful processing of many kinds of time sequence benefits from the effectivemodeling of the sequence，such as Linear Processing Coding(LPC) model and Code-Excited LinearPrediction(CELP) model in speech processing area,Hidden Markov Model(HMM)and GaussianMixture Model(GMM) in recognition area.The speech processing technology can’t be widely usedwithout the effective modeling of the sequence.As a new technology to substitute the Nyqusitsampling technology,CS system must find a proper model of the measurements,and this is thebackground and starting point of the thesis.Firstly, the thesis analysis the effect of the measurement matrix to the modeling method of theCS measurements and puts forward a new criterion for the choice of the measurement matrix, thecriterion suggests that we don’t have to choose the measurement matrix with the highestcompression ratio. In fact, in order to further process the measurements, we should choose the onewhich is most suitable for modeling. Autocorrelation function is used to decide whether themeasurements are suitable for modeling. After a study of many kinds of the measurement matrix,the thesis finally chooses the row echelon measurement matrix, and applies the LPC model,sinusoidal model, and curve fitting model to the measurements.But experiments show that all theabove classic models can’t model the CS measurements effectively, due to the fact that theprojection process damages the original features of the speech signal.To solve the problem, wemust find a new and effective model of the CS measurements. Secondly, the thesis researches basic theory of sparse decomposition.Considering that there iscertain feature and law in the CS measurements, the thesis proposes a sparse decomposition methodbased on a redundant dictionary to model the measurements. Due to the better performance of thesinusoidal model, the thesis constructed a dictionary with the elements of sines. Considering theactual scene where speech processing takes place, the thesis chooses the series of Matching Pursuitalgorithms. After a comparison of Matching Pursuit (MP) algorithm and Orthogonal MatchingPursuit (OMP) algorithm, the thesis chooses OMP algorithm. Experiment results show that thesinusoidal dictionary decomposition based on OMP method can model the measurementseffectively.Thirdly, the thesis did some researches on the robustness of the new model.Speech signal isalways mixed with the background noise, and the noise is usually magnified, expanded anddistorted through the measurement matrix, which inevitably injures the performance of thereconstructed voice,so a practical CS measurement modeling method must take the effect of thenoise into consideration.Researches on the step of compressing and sensing indicatesthat,compared with the other measurement matrix, the row echelon measurement matrix canenhance the signal but reduce the noise. However, common algorithms shows that the performanceof the reconstructed voice is still worth than the one without noise, that’s to say, the anti-noiseperformance of the modeling method must be considered of. The thesis analysis the classification ofthe common noise, and focuses on the reduction of additive white gaussian randomnoise.Experiment results show that the modeling method can improve the quality of thereconstructed speech signal in the background of strong noise, this indicates that whether for thepurpose of compressing or anti-noise ability, the sinusoidal dictionary model based on OMPmethod is helpful for the application of the CS theory.