基于压缩感知的双向阈值匹配追踪算法

最近提出的前向后向算法(Forward-backward Pursuit,FBP)因为重构精度较高受到人们更多关注.但是FBP算法没有考虑到当前迭代残差信号的变化,每次迭代选取的原子和删减原子的数目是固定的.鉴于此,提出了双向阈值匹配追踪算法(Ovonic Threshold Matching Pursuit,OTMP).OTMP前向原子选择过程通过限制等距性质(RIP)和残差的条件选出部分新增加原子,在回溯过程中通过当前迭代的重构水平剔除可能错误的原子.实验表明,在一定条件下OTMP时间复杂度和正交匹配追踪算法(Orthogonal Matching Pursuit,OMP),子空间追踪算法(Subspace Pursuit,SP)相当,重构精度明显高于SP,FBP算法和其他几种贪婪算法.

Ovonic Threshold Matching Pursuit for Sparse Signal Reconstruction Based on Compressed Sensing

Greedy algorithm is used widely for its fast reconstruction performance in compressed sensing process.Due to independent error correction, the greedy pursuits with the idea of backtracking has a more accurate reconstruction ability. Forward-backward Pursuit algorithm (FBP) has received more attention because of its high accuracy in signal reconstruction. However, FBP does not take the change of signal into consideration and the number of selecting atoms or pruning atoms in each iteration is constant. As a result, Ovonic Threshold Matching Pursuit (OTMP) is put up. On the one hand, OTMP tries to pick out part new atoms by a threshold which is concerned with the Restricted Isometry Property and residual condition in the forward atom selection process. On the other hand, based on reconstruction level of current iteration, OTMP deletes some atoms which are probably wrong by a new threshold. For one thing, unlike SP, OTMP does not need the sparse degree of original signal. For another, unlike FBP, the number of selecting atoms or deleting atoms is related to the signal in current iteration. The experimental result shows that under certain condition, time complexity of OTMP is comparable with OMP, SP. Meanwhile, the reconstruction accuracy of OTMP surpasses SP, FBP and other greedy algorithms obviously.