基于混合采样的图像分块压缩感知方法

A method for block compressed sensing of images based on hybrid sampling

针对图像压缩感知问题，提出一种基于混合采样的分块压缩感知方法——HBCS方法。该方法利用基于随机采样和低分辨率采样构造的混合采样矩阵和分块策略，有效地提高了图像采样效率和重构性能。理论证明：混合采样矩阵具有低分辨率采样的直接测量图像低频信息的特性和随机采样的近似最优的重构功能，且以高概率与大多数固定稀疏基不相干，结构简单，非常易于实现；分块策略能保证算法复杂度不随图像尺寸而改变，适合实时处理高分辨率图像。实验结果表明，在相同采样值数目下，该方法采用总变差（TV）重建算法时的重构质量尤其是在图像低频信息恢复方面明显优于其它已有方法。

The compressed sensing of images was studied, and a new method for block compressed sensing （BCS） of im- ages based on Hybrid sampling, called the HBCS for short, was proposed to improve the performance of image re- construction. The method uses a hybrid sampling matrix random sampling （RS） and low-resolution sampling （LRS） to complementally measure the image information data with the high sensing efficiency. The hybrid sampling matrix with a simple structure was proved theoretically to be incoherent with most fixed sparsity bases. And the block strategy of the method ensures that the complexity of measurement and reconstruction processes does not change with the image size, so the method is simple and easy to implement, and is suitable for large-scale applica- tions. The experimental results show that the proposed method can achieve much better results than many state-of- the-art algorithms in terms of both PSNR and visual perception when using the total variation （TV） reconstruction algorithm.