School of Computer Science and Technology and the Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi'an, China.
IEEE Trans Image Process. 2011 Jul;20(7):1904-11. doi: 10.1109/TIP.2010.2104159. Epub 2011 Jan 17.
Compressive sensing (CS) is a theory that one may achieve an exact signal reconstruction from sufficient CS measurements taken from a sparse signal. However, in practical applications, the transform coefficients of SAR images usually have weak sparsity. Exactly reconstructing these images is very challenging. A new Bayesian evolutionary pursuit algorithm (BEPA) is proposed in this paper. A signal is represented as the sum of a main signal and some residual signals, and the generalized Gaussian distribution (GGD) is employed as the prior of the main signal and the residual signals. BEPA decomposes the residual iteratively and estimates the maximum a posteriori of the main signal and the residual signals by solving a sequence of subproblems to achieve the approximate CS reconstruction of the signal. Under the assumption of GGD with the parameter 0 < p < 1, the evolutionary algorithm (EA) is introduced to CS reconstruction for the first time. The better reconstruction performance can be achieved by searching the global optimal solutions of subproblems with EA. Numerical experiments demonstrate that the important features of SAR images (e.g., the point and line targets) can be well preserved by our algorithm, and the superior reconstruction performance can be obtained at the same time.
压缩感知（CS）理论指出，对于稀疏信号，只要从信号中获取足够数量的压缩感知测量值，就可以实现对原始信号的精确重建。然而，在实际应用中，SAR 图像的变换系数通常具有较弱的稀疏性，精确重建这些图像极具挑战性。本文提出了一种新的贝叶斯进化追踪算法（BEPA）。该算法将信号表示为主要信号和一些残差信号的和，并且将广义高斯分布（GGD）作为主要信号和残差信号的先验分布。BEPA 对残差进行迭代分解，并通过求解一系列子问题来估计主要信号和残差信号的最大后验概率，从而实现信号的近似 CS 重建。在参数 0 < p < 1 的 GGD 假设下，首次将进化算法（EA）引入 CS 重建。通过 EA 搜索子问题的全局最优解，可以实现更好的重建性能。数值实验表明，我们的算法可以很好地保留 SAR 图像的重要特征（例如，点目标和线目标），同时获得更好的重建性能。
