Research On Algorithms Of Signal Reconstruction And Classification Based On Compressive Sensing

Compressive Sensing which develops from the fundamental premise named sparserepresentation, breaking the normal pattern in the traditional signal processing of firstsampling and then compress, using the sampling rate which is far below the request ofShannon theorem to sampling the signal when the compression is finished at the sametime. It is a new frame of signal processing cutting down the cost of sampling、storageand process. Based on the theory of Compressive Sensing, this dissertation focuses onthe research of various algorithms for the signal reconstruction and classification, aswell as choose the S transform as the time-frequency filtering tool for the denoisingpretreatment, in the purpose of reducing the impact of the noise on the signalreconstruction and classification.For signal denoising, propose the generalized directional S transform byintroducing the varying-tendency window and the directional parameter, and thenincorporating spectral subtraction and threshold processing proposes the denoisingmethod based on the generalized directional S transform. The experimental resultsvalidate the advantage of the proposed method over denoising, taking it further, theproposed method can provide effective denoising pretreatment for the subsequentreconstruction and classification.For signal reconstruction based on the CS, analysis and comparisons are made tothe classical signal reconstruction algorithms, including Iteratively Reweighted LeastSquares in the convex relaxation, Matching Pursuit、Orthogonal Matching Pursuit、Compressive Sampling Matching Pursuit and Subspace Pursuit in the greedy pursuitalgorithm. Experiments validate the feasibility of the signal reconstruction methodbased on CS、the superiority of the transform matrix which train from the KSVDalgorithm、 the improvement of the reconstruction probability with the proposeddenoising method.For signal classification based on the CS, for the drawbacks of the traditionalreconstruction algorithms that it only can be applied to the unsupervised classification,due to the reason that its objective function only consists of reconstruction error itemand sparse item, propose a supervised classification algorithm applied to signalclassification by introducing the Fisher discrimination item into the object function.Further, for the limitation of the SKSVD that different classes may be have intersection, obtaine the MSKSVD algorithm by modifying the atom set of the SKSVD, in whichdifferent classes have mutually disjunct atom sets, while the atom in the same class islinear independence. The experimental results show the superiority of the MSKSVDover classification performance compared with other algorithm, and the robustness ofthe MSKSVD to different parameter、training set rate、sparse dimension and the SNR.