L_p范数压缩感知图像重建优化算法

Improved search algorithm for compressive sensing image recovery based on L_p norm

目的压缩感知理论中的重构算法作为关键技术之一,在科学研究方面起到了关键的作用。常用的重构算法包括L_0范数的非凸优化算法和L_1范数的凸优化算法,但它们的缺点是重构精度不高,运算时间很长。为了克服这一缺陷,提高现有基于L_p范数的压缩感知图像重构算法的重建精度和算法效率,本文提出改进算法。方法针对拉格朗日函数序列二次规划(SQP)方法中海瑟(Hesse)矩阵不正定导致计算量很大的问题,引入价值函数,修正Hesse矩阵的序列二次规划方法并结合图像分块压缩感知技术,提出了一种基于L_P范数压缩感知图像重构算法。结果在采样率同为40%情况下,本文算法下的信噪比为34.28 dB,高于BOMP(block orthogonal matching pursuit)算法信噪比2%,高于当罚函数作为修正方法时的13.2%。本文算法计算时间为190.55 s,快于BOMP算法13.4%,快于当罚函数作为修正方法时的67.5%。采样率同为50%的情况下,本文算法下的信噪比为35.42 dB,高BOMP算法信噪比2.4%,高于当罚函数作为修正方法时信噪比12.8%。本文算法的计算时间是196.67 s,快于BOMP算法68.2%,快于81.7%。在采样率同为60%的情况下,本文算法的信噪比为36.33 dB,高于BOMP算法信噪比3.2%,高于当罚函数作为修正方法时信噪比8.2%。本文算法计算时间为201.72 s,快于BOMP算法82.3%,快于当罚函数作为修正方法时86.6%。在采样率为70%的情况下,本文算法信噪比38.62 dB,高于BOMP算法信噪比2.5%,高于当罚函数作为修正方法时信噪比9.8%。本文算法计算时间为214.68 s,快于BOMP算法88.12%,快于当罚函数作为修正方法时的91.1%。实验结果显示在相同的采样率的情况下,本文改进算法在重构精度和算法时间上均优于BOMP算法等其他算法。并且采样率越高,重构图像精度越来越高,重构算法时间越来越短。结论通过实验对本文算法、BOMP重构算法等其他算法在信噪比和算法计算时间进行对比,在不同采样率下,本文算法都明显优于其他两种算法,而且在采样率仅为20.5%时,信噪比高达85.154 3 dB,重构图像比较清晰。本文算法的最大优点在于采用了分块压缩感知技术,提高图像重构效率,降低了重构时间,缺点是在图像采样率比较低的情况下,存在图像干扰块效应。接下来研究方向是如何在采样率低的情况下,高精度地还原图片,消除图像干扰块效应。

Objective As one of the key technologies in compression sensing, a reconstruction algorithm plays a key role in scientific research. Commonly used reconstruction algorithms include the non-convex optimization algorithm based on L0 norm and the convex optimization algorithm based on L1 norm. However, these algorithms exhibit shortcomings, such as low precision reconstruction and extremely long operation time. To overcome these limitations and improve the precision and efficiency of the existing compressed sensing image reconstruction algorithm based on Lp norm reconstruction, an improved al- gorithm is presented in this study. Method Sequential quadratic programming is one of the most effective methods for sol-ving constrained nonlinear programming problems in recent years. Compared with other algorithms, it demonstrates the most apparent advantages of good convergence, high computational efficiency, and edge search capability. The use of the La- grange function series quadratic programming （SQP） method for the heather （Hesse） does not provide a positive definite matrix calculation for many problems; therefore, a value function should be introduced, the Hesse matrix sequence quadratic programming method should be corrected, and an image block compressed sensing technology should be integrated. This study proposes an image reconstruction algorithm based on Le norm compression awareness. Result Under the same sam- pling rate of 40% , the signal-to-noise ratio （SNR） of the proposed algorithm is 34. 28 dB, which is better than that of the block orthogonal matching pursuit （BOMP） algorithmThe BOMP algorithm＇ s SNR is 33.76dB） and the algorithm presen- ted when the penalty function is used as the correction method （30. 23 dB）. The time of the proposed algorithm is 190. 55 s, which is faster than that of the BOMP algorithm （302. 14 s） and that when the penalty function is used as the correction method （586. 15 s）. When the sampling rate is 50% , the SNR of the proposed algorithm is 35.42 dB, which is better than that of the BOMP algorithm （34. 56 dB） and that when the penalty function is used as the correction method （31.38 dB）. The computation time of the proposed algorithm is 196. 67 s, which is faster than that of the BOMP algorithm （617.62 s） and that when the penalty function is used as the correction method （ 1 071.15 s）. When the sampling rate is 60% , the SNR of the proposed algorithm is 36. 33 dB, which is better than that of the BOMP algorithm （35.18 dB） and that when the penalty function is used as the correction method （ 33.57 dB）. The computation time of the proposed algorithm is 201.72 s, which is faster than that of the BOMP algorithm （ 1 136. 29 s） and that when the penalty function is used as the correction method （ 1 505. 35 s）. At a sampling rate of 70% , the SNR of the proposed algorithm is 38. 62 dB, which is better than that of the BOMP algorithm （ 37.65 dB ） and that when the penalty function is used as the correction method （35.17 dB）. The calculation time of the proposed algorithm is 214. 68 s, which is faster than that of the BOMP algorithm （1 802.42 s） and that when the penalty function is used as the correction method （2 415.81 s）. Experimental results show that the improved algorithm is superior to the BOMP algorithm and algorithm when the penalty function is used as the correction method in terms of reconstruction precision and calculation time under the same sampling rate. When the sam- piing rate is higher, the precision of the reconstructed image will be higher and reconstruction time will be shorter. Conclusion The convex optimization algorithm for image reconstruction based on compression perception theory is superior to the non-convex optimization algorithm for image reconstruction. However, reconstruction precision emains low and re- construction rate emains slow, and thus, the problem remains serious. This study proposes an image reconstruction algo- rithm based on Lp norm compression awareness. Experiment results indicate that the proposed algorithm generally improves image reconstruction precision and computation time. Further study should be conducted to establish an algorithm with higher precision and faster image reconstruction.