- 學位論文
一般化二維小波轉換及影像多重解析分析
Multiresolution Analysis for Image by Generalized 2-D Wavelets
並列摘要
The most important feature of the wavelet transform is that we can use few wavelet coefficients to approximate a signal. Because of this property, JPEG 2000 adopted the wavelet transform as a portion of its algorithm. However, the fundamental theory of this feature was derived from one-dimensional signals. For two-dimensional signals, we can use “separable wavelet transform” to extend one-dimensional wavelet transform into two-dimensional wavelet transform. Although this method was used widely, it ignored the geometric properties of the two-dimensional signal such as edges. Since two-dimensional signals have more features, many researchers started to propose a new transform such that the new transform not only has all features of the wavelet transform but also exploit the properties of the two-dimensional signals. Furthermore, the performance is better than that of the separable wavelet transform. This thesis focuses on the ideas, advantages, and disadvantages of these new transforms. After discussing these methods, we propose our method to improve the performance.