Matched Wavelet Detection And Multiscale Geometry Analysis In Image

Wavelet transform has been widely used. Using the best wavelet base is anticipantfor us, but it is difficult to design a wavelet base matched the signal well. At the sametime, along with the perfecting of wavelet theory, we find that wavelet is the optimalbases for the functions having point shape singularity, and its coefficients are sparse.But, in high dimensional cases, wavelet analysis cannot take full advantages of thegeometrical features that data contained themselves. It is not the optimal or the sparsestrepresentation of the functions and always damages anisotropic edges information inimages.Based on all of these, the thesis has been down as follow:It is widely believed that we can use the wavelet technique to efficiently deal withecho signals in pulse echo reflection system. In order to obtain the best results, thewavelet bases matching to desire signals are expected. But it is difficult to detect thesignals when small signal to noise ratios (SNR) because of completelymatched waveletbases not existing. In this paper we put forward a new concept of detecting echosignals, that is, Wavelet Signal Detection. We construct the wavelet functions as thetransmitting signals, and the echo signal is processed with the correspondingcompletely same wavelet base. The new detection method is effectively to deal withthe low SNR echoes. The simulation of the ultrasonic detection indicates the validity ofthe new way. The numerical results show good detection even for SNR of -17db. Hence,it can detect the echo signals completelyburied in noises.The conventional wavelet transform technique is efficient when dealing with 1-Dsignals. But for 2-D images with abundant geometry texture information, the standard2-D separable wavelet transform is not satisfying because of its direction absence. Inorder to obtain a better image representation, we present the concept of the directionwindows. It can help us to obtain the direction in images. Based on these, we putforward a novel image de-noising method in terms of the intrinsic geometrycharacteristics of images. Based on the minimal approximation error, we search thegeometry directions in each initialized direction windows, and combine smallerwindows with a bigger one according to the regulation of PSNR. When the bestdenoising directions are obtained, we project 2-D information to 1-D along the certaindirections and perform 1-D wavelet transform to denoise. The validity and efficiency...