基于自适应分块和联合优化光滑l_(0)范数的二维压缩感知算法

2D Compressed Sensing Algorithm Based on Adaptive Blocking and Joint Optimization Smooth l_(0) Norm

传统的压缩感知模型和重构方法,虽能有效减少数据量,但压缩和重构性能不佳,故该文提出一种基于自适应分块和联合优化光滑l_(0)范数(SL0)的2维压缩感知算法。压缩过程利用灰度熵和四叉树算法进行自适应分块和采样率分配,同时对压缩模型改进,使用混沌循环矩阵作为测量矩阵,提升了压缩性能。重构过程基于SL0算法,采用陡峭性更高的拟合函数,结合拟牛顿法和动态迭代的方案提高重构质量和效率。该算法峰值信噪比和结构相似性指数相比现有算法平均提升了5.44 dB和21.08%,平均计算时间仅需1.59 s,表明该算法能稳定、快速地实现图像的压缩感知和精确重构,为压缩感知和图像重构提供了新方法。

A 2-dimension compressed sensing algorithm based on adaptive blocking and joint optimization Smooth l_(0)(SL0)norm is proposed to solve the problem of poor compression and reconstruction performance of the traditional compressed sensing model and reconstruction method.In the compression process,gray entropy and quadtree algorithm are used for adaptive blocking and sample rate allocation.At the same time,the compressed sensing model is optimized and the chaotic cyclic matrix is used as the measure matrix,which improves the compression performance.In the reconstruction process based on SL0 algorithm,a fitting function with higher steepness and a scheme combined with Quasi-Newton method and dynamic iteration are adopted to improve the reconstruction quality and efficiency.Compared with other algorithms,the peak signal to noise ratio and structural similarity index of the proposed algorithm are improved by 5.44 dB and 21.08%on average respectively.The average calculation time is only 1.59 s.Based on realizing image compression and accurate reconstruction stably and quickly,the proposed algorithm provides a new method for compressed sensing and image reconstruction.