One of the distinguished properties of the discrete wavelets transform is that the major dominant factors can be extracted from the data. We have applied this property to the data compression and reducing the noise data. In the present paper, we have tried to shrink and enlarge the color image data in static as well as dynamic states by means of the vector wavelets transform. Key idea is that the color image data are represented in terms of the 3dimensional vector data by corresponding the red, green and blue orthogonal components of the image to the 3dimensional orthogonal x, y and z components. Several examples demonstrate the usefulness of our new method to work out the graphical communication tools.
A discrete wavelet transform is one of the effective methodologies for compressing the image data and extracting the major characteristics from various data, but it always requires a number of target data composed of a power of 2. To overcome this difficulty without losing any original data information, we propose here a novel approach based on the Fourier transform. The key idea is simple but effective because it keeps all of the frequency components comprising the target data exactly. The raw data is firstly transformed to the Fourier coefficients by Fourier transform. Then, the inverse Fourier transform makes it possible to the number of data comprising a power of 2. We have applied this interpolation for the wind vector image data, and we have tried to compress the data by the multiresolution analysis by using the three-dimensional discrete wavelet transform. Several examples demonstrate the usefulness of our new method to work out the graphical communication tools.
This paper describes that key idea to introduce wavelets transform, one-.two-and. three-dimensional wavelets transforms are introduced by means of Daubechies 2nd order base function. Finally, nth order bi-orthogonal wavelets transform algorism is derived in terms of tensor notation. As a result, it is clarified the mathematical as well as physical meaning of the discrete wavelets transform. Thus, this paper suggests that various signal and image processing problems can be carried out by the discrete wavelets transform.
A suitable selection of base functions for discrete wavelets transform is a difficult problem for data analysis. The grouping frequencies derived from the analysis are often dependent on the base functions and a selection of the base functions has been made mostly by trial and error. On the selection of the most suitable model from several statistical models, the model of which AIC (Akaike Information Criterion) is minimum, is selected as the suitable model. In this study, we propose the application of the AIC as the methodology for selecting the most suitable model for data compression on wavelets transform, that is, the compressions of one and two dimensional data are made by wavelets transform, and we select the minimum AIC model as the suitable one. The same method is applied to the analysis of the global wind, and we see that it can be also valid for an evaluation of the efficiency of data compression. The suitable selection of the base functions which reflects a characteristic of the data is constructed by the relation between the order of the base functions and the suitable model selected by AIC.Akaike information criterion, Wavelets transform, Multi resolution analysis
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