Abstract: The key of reconstruction algorithm based on CS is to exactly resume the original high-dimension-data from low-dimension measurement. Aiming at most algorithms acquiring the sparsity as a prior, a backward and fixed step size adaptive matching pursuit reconstruction algorithm is presented, which can acquire exact reconstruction without prior information of sparsity. A fixed and biggish step size is set to make sure the size of support set of the signal to be increased stably and quickly. The energy difference between adjacent reconstructed signals is taken as the halting condition for iteration. A standard regularized method is employed to post-dispose the final iteration result, which backward eliminates superfluous atoms to acquire exact reconstruction. Experimental results show that this algorithm can quickly acquire exact reconstruction with sufficient measurements.

Key words: compressed sensing, sparsity, support set

摘要： 基于压缩感知理论的重建关键在于从压缩感知得到的低维数据中精确恢复出原始的高维稀疏数据。针对目前大多数算法都建立在稀疏度已知的基础上，提出一种后退型固定步长自适应匹配追踪重建算法，能够在稀疏度未知的条件下获得图像的精确重建。该算法通过较大固定步长的设置，保证待估信号支撑集大小的稳步快速增加；以相邻阶段重建信号的能量差为迭代停止条件，在迭代停止后通过简单的正则化方法向后剔除多余原子保证精确重建。实验结果表明，该算法在保证测量次数的条件下可以获得快速的精确重建。

关键词: 压缩感知, 稀疏度, 支撑集