基于解析轮廓波变换的图像稀疏表示及其在压缩传感中的应用

Sparse Image Representation Using the Analytic Contourlet Transform and Its Application on Compressed Sensing

提出了具有平移不变性的低冗余度解析轮廓波变换.在该变换中圆对称滤波器组首先将图像分解为多个不同分辨率的细节子带和一个低频子带,再对细节子带进行希尔伯特变换形成二维解析信号.最后用方向滤波器组对二维解析信号进行分解,实现具有平移不变性多尺度多方向的解析轮廓波变换.解析轮廓波变换基函数的实部和虚部与Gabor小波的实部和虚部类似,符合人眼视觉特性.实验结果表明解析轮廓波变换在图像去噪和压缩传感方面具有明显优势.

The translation invariant analytic contourlet transform with low redundancy is proposed.In this transform,the circular symmetric filter banks decomposes image into multi-resolution detail subbands and one low-frequency subband,then the detail subbands are processed by Hilbert transform to generate two dimensional analytic signals.At last,the analytic signals are decomposed by directional filter bank to implement analytic contourlet transform with multi-scale,multi-direction,and translation invariant property.The real part and imaginary part of the analytic contourlet basis functions resemble Gabor wavelet,and conform well to the human visual system.The experiments show that the analytic contourlet transform can achieve higher performance in image denoising and compressed sensing.