利用小波系数上下文建模的Bayesian压缩感知重建算法

A Bayesian Compressive Sensing Reconstruction Algorithm Using Wavelet-Domain Context Modeling

针对目前压缩感知图像重建算法没有充分利用图像小波系数尺度内相关性的缺点,提出一种上下文建模的Bayesian压缩感知重建(CBCS)算法。该算法假定图像的小波系数服从参数未知的spike-and-slab概率模型,先通过一种新的上下文建模方法得到待估计小波系数邻域内的上下文矢量,然后根据待估计系数与上下文矢量的相关性及其父亲系数的状态,推测待估计系数为显著系数的概率,最后根据待估计系数的概率,采用马尔科夫链-蒙特卡洛采样的Bayesian推理从观测向量中恢复出图像的小波系数,进而得到重建图像。实验结果表明,CBCS算法可以自适应于图像内容的变化,与仅利用尺度间相关性的小波树结构的压缩感知重建算法相比,在0.9的采样率下,重构性能最大可提高近2dB。

A novel Bayesian compressive sensing image reconstruction algorithm based on the context modeling is proposed to solve the problem that the intrascale dependencies of image＇s wavelet coefficients is not fully exploited by the compressive sensing reconstruction algorithm.It is assumed that the wavelet coefficients of image obey a spike-and-slab probability model.Context vectors in the current coefficient＇s neighborhood are obtained through a new context modeling method.Then,the significant probability of current coefficient is estimated according to the dependencies of the context vector with the current coefficient and the state of parent coefficient.Finally,the image＇s wavelet coefficients is recovered from the observation vector based on the significant probabilities of the image＇s wavelet coefficients by using a Bayesian inference via Markov chain Monte Carlo sampling,thus,the reconstruction image is generated.Since the spike-and-slab probability model with context modeling is adaptive to the spatial changes of the images,experimental results and comparisons with Bayesian tree-structured wavelet compressive sensing algorithm which only uses the interscale dependencies show that the proposed algorithm improves the peak-signal-to-noise-ratio nearly by 2 dB at the sampling rate of 0.9.