结合稀疏贝叶斯学习 (SBL)和可压缩传感理论(CS)，给出一种在噪声测量条件下重建可压缩图像的方法。该方法将CS理论中图像重建过程看作一个线性回归问题，而待重建的图像是该回归模型中的未知权值参数；利用SBL方法对权值赋予确定的先验条件概率分布用以限制模型的复杂度，并引入超参数；最大化超参数的边缘对数似然函数求得权值参数的最优估计即待重建图像。该方法同时还给出了权值估计的后验概率密度和误差条，从而获得权值最优值的不确定性测量。实验结果表明，SBL方法可以获得精确重建，并且在相同相对重建误差的条件下，比基追踪(BP)方法需要更少的重建时间，比正交匹配追踪(OMP)需要更少的测量次数。

Combining sparse bayesian learning (SBL) with compressed sensing (CS), a new method of reconstruction for compressed images with contaminated measurements is presented. This method regards the process of image reconstruction as a linear regression model and the image to be reconstructed as the unknown weights of the regression model. By sparse bayesian learning, the weights are endowed with certain prior condition probability density function, which limits the complexity of the model and simultaneously introduces the hyper-parameters. With maximizing the marginal likelihood function of hyper-parameters, the optimal weights are acquired, i.e. the reconstructed image. Simultaneously, this method provides the posterior probability density and the error bars of estimated weights, which deduces the uncertainty of reconstruction. Experimental results show that the new method can acquire exact reconstruction and under the same relative error of reconstruction, it is superior to basis pursuit on reconstruction time and orthogonal matching pursuit on the number of measurements.