Noise reduction using wavelet cycle spinning: analysis of useful periodicities in the z-transform domain

Cycle spinning (CS) and a'trous algorithms are different implementations of the undecimated wavelet transform (UWT). Both algorithms can be used for UWT and even though the resulting wavelet coefficients are different, they keep a correspondence. This paper describes an analysis of the CS algorithm performed in the z-transform domain, showing the similarities and differences with the a'trous implementation. CS generates more wavelet coefficients than a'trous, but the number of significative and different coefficients is the same in both cases because of the occurrence of a periodic repetition in CS coefficients. Mathematical expressions for the relationship between CS and a'trous coefficients and for CS coefficient periodicities are provided in the z-transform domain. In some wavelet denoising applications, periodicities (present in the coefficients of the CS procedure) can also be found in the performance measure of the processed signals. In particular, in ultrasonic CS denoising applications, periodicities have been appreciated in the signal-to-noise ratio (SNR) of the ultrasonic denoised signals. These periodicities can be used to optimize the number of CS coefficients for an efficient implementation. Two examples showing the periodicities in the SNR are included. A selection of several reduced sets of CS wavelet coefficients has been utilized in the examples, and the SNRs resulting after denoising are analyzed.This work was partially supported by Spanish MCI Project DPI2011-22438 and MEC Project TIN2013-47272-C2-1-R. The translation of this paper was funded by the Universitat Politecnica de Valencia, Spain.Rodríguez-Hernández, MA.; San Emeterio, JL. (2016). Noise reduction using wavelet cycle spinning: analysis of useful periodicities in the z-transform domain. Signal, Image and Video Processing. 10(3):519-526. https://doi.org/10.1007/s11760-015-0762-8S519526103Daubechies, I.: Ten Lectures on Wavelets. 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Timor Leste Tais Motif Recognition Using Wavelet and Backpropagation

Timor Leste is a new country of the 21st century in Southeast Asia that has a diverse culture. Tais Timor Leste has a high historical value as well as cultural identity. It is also one of the cultural heritages of Timor Leste. Tais Timor has its own characteristics and meanings in every motif, but there are still many communities of Timor Leste as well as foreign tourists who do not know the variety of the motif. Therefore, this study aimed to establish the system recognition of Tais Timor motif through the image based on the type of motif. The wavelet transform is used in the process of feature extraction and image decomposition to obtain coefficient values of which the value of energy and entropy will then be calculated. For the recognition of Tais Timor motif, backpropagation algorithm was used. This application is built using MATLAB programming language. The analysis and testing of these studies show that the accuracy of recognition of Tais Timor motif with 4 testing parameters got recognition accuracy and presentation of 80%. Thus the motif used can be identified by using both wavelet transform and backpropagation algorithm