基于二维DFT域全相位滤波的图像多分辨率分析

Multiresolution analysis of image based on 2D all-phase filtering in DFT domain

图像多分辨率分析在信号滤波、图像除噪、图像融合、图像边缘检测领域中应用广泛。该文设计了一种新的图像多分辨率分析方法,通过对全相位系统函数进行谱分解,实现了基于全相位的严格功率互补的高低通滤波器设计,按照全相位处理的基本理论,选择不同的正交变换方式和基窗函数可以方便地设计出具有不同分析/合成效果的全相位波包。实验表明,DFT域全相位分析滤波器可以实现对图像的多层分解,由合成滤波器还原得到的图像误差几乎为零。在图像数据压缩、自适应除噪方面具有较为广泛的应用前景。

Multiresolution analysis method in images is widely applied in signal filtering,image de-noising,fusion and edge detecting.This paper presents a novel way to implement multiresolution analysis.Absolute power comlementary high-pass and low-pass filters are designed by decompose the spectrum of the transmisson characteristic of all-phase system.In term of all-phase theory,all-phase wave packets with various analysis and synthesis results can be easily derived by using different orthogonal transformation and base window.Finally a simulation test is given to verify that all-phase analysis filter in DFT domain can be used in multi-layer resolution of image and error from the recovered image by means of all-phase systhesis is as low as-40 dB and more.This novel method will be more widely applied in the filed of image compression and adaptive de-nosing etc.