Discrimination theory of wavelet filters with learning ability

具有学习能力的小波滤波器判别理论

• 批准号: 11558039
• 负责人: NIIJIMA Koichi
• 金额: $ 8.26万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11558039/
• 关键词: lifting wavelet filter; free parameter; learning method; learning ability; extraction; noise reduction; multiresolution analysis; 3D surface generation; 学習方式; 特定信号; ダイアディックウェーブレット; フィルタ; 抽出; メッシュ単純化アルゴリズム; メッシュ細分化アルゴリズム; 学習理論; 地磁気水平成分; 磁気

Wavelet filters with learning ability indicate lifting wavelet filters proposed by Sweldens who is a researcher at Lucent Technology in USA. The lifting wavelet filters are consist of biorthogonal analysis and synthesis filters. A signal is decomposed into lowpass and highpass components using the analysis filter, and the original signal can be reconstructed from the lowpass and highpass components using the synthesis filter. This means that the original signal is equivalent to the decomposed lowpass and highpass components. The lifting wavelet filters are constructed by adding lifting filters to biorthogonal wavelet filters. The lifting filter contains free parameters which can be determined adaptive to signals and images.In our research, we proposed several learning methods of the free parameters adaptive to specific parts of signals and images, and established a discrimination theory for extracting pieces similar to the specific parts. We also presented an impulse noise reduction method based on our learning method. Furthermore, we proposed a fast simplification algorithm for generating 3D surfaces by using an idea of multiresolution analysis of wavelets.

具有学习能力的小波滤波器是指美国朗讯科技公司研究员Sweldens提出的提升小波滤波器。提升小波滤波器由双正交分析滤波器和合成滤波器组成。使用分析滤波器将信号分解为低通和高通分量，并且可以使用合成滤波器从低通和高通分量重建原始信号。这意味着原始信号等效于分解的低通和高通分量。提升小波滤波器是通过在双正交小波滤波器上添加提升滤波器来构造的。提升滤波器包含可以适应信号和图像的自由参数。在我们的研究中，我们提出了几种适应信号和图像特定部分的自由参数的学习方法，并建立了提取与特定部分相似的片段的判别理论。我们还提出了一种基于我们的学习方法的脉冲噪声降低方法。此外，我们提出了一种利用小波多分辨率分析思想生成 3D 表面的快速简化算法。

项目成果

K.Niijima and K.Kuzume: "Wavelets with convolution-type orthogonality conditions"IEEE Transactions on Signal Processing, 47-2. 47-2. 408-421 (1999)

K.Niijima 和 K.Kuzume：“具有卷积型正交性条件的小波”IEEE 信号处理汇刊，47-2。

K.Kuzume, S.Takano, K.Niijima: "Integer-type Haar lifting wavelet processor for signal detection"Proceedings of the IASTED International Conference on Intelligent Systems and Control, ACTA Press. 480-485 (2001)

K.Kuzume、S.Takano、K.Niijima：“用于信号检测的整数型 Haar 提升小波处理器”IASTED 国际智能系统与控制会议论文集，ACTA 出版社。

K.Niijima, S.Takano: "Finding of signal and image by integer-type Haar lifting wavelet transform"Progresses in Discovery Science, Springer. (in press). (2002)

K.Niijima、S.Takano：“通过整数型 Haar 提升小波变换查找信号和图像”，Discovery Science 进展，Springer。

新島耕一: "ウェーブレット画像解析"科学技術出版. 313 (1999)

新岛浩一：《小波图像分析》科学技术出版社313（1999）。

K.Kuzume, K.Niijima, S.Takano: "Signal detection based on lifting wavelet and its application to ECG signal processing"Proceedings of the 22nd IASTED International Conference on Modeling, Identification, and Control (MIC2003). 299-303 (2003)

K.Kuzume、K.Niijima、S.Takano：“基于提升小波的信号检测及其在 ECG 信号处理中的应用”第 22 届 IASTED 国际建模、识别和控制会议 (MIC2003) 论文集。