QR分解-凸集投影协同超分辨率重建

doi:10.12305/j.issn.1001-506X.2026.05.03

摘要/Abstract

摘要：

针对线阵推扫成像中因目标-平台相对运动导致的亚像素位移与过采样信息冗余问题，提出一种融合物理先验与数值优化的超分辨率重建方法。首先，基于目标运动速度与平台参数推导过采样比例及最优超分辨率倍数。其次，通过构造正则化增广矩阵的正则化QR分解实现病态方程组的稳定求解，抑制噪声放大与伪影生成。最后，结合凸集投影方法嵌入成像系统的时空耦合约束，实现细节增强与物理一致性重建。仿真实验表明，该方法在红外遥感影像中可将局部结构相似性指数提升至0.8402，光谱复原的相对均方根误差降低80.17%，优于传统广义逆与迭代插值算法，41个光谱通道的处理总耗时低于150 ms，验证了其在高光谱数据处理的工程实用价值。

关键词: 线推扫过采样, 超分辨率重建, 正则化QR分解, 凸集投影法

Abstract:

A super-resolution reconstruction method integrating physical priors and numerical optimization is proposed to address the sub-pixel displacement and oversampling information redundancy caused by target-platform relative motion in push-broom imaging. Firstly, the oversampling ratio and optimal super-resolution factor are derived based on target motion velocity and platform parameters. Secondly, stable solutions for ill-posed equations are achieved through regularized QR decomposition of regularized augmented matrices, suppressing noise amplification and artifact generation. Finally, spatiotemporal coupling constraints of imaging systems are embedded via the projection onto convex sets method, realizing detail enhancement and physically consistent reconstruction. Simulation experiments demonstrate that this method improves the local structural similarity index to 0.8402 in infrared remote sensing imagery, while reducing the relative root mean square error of spectral restoration by 80.17%, outperforming conventional generalized inverse and iterative interpolation algorithms. The total processing time for 41 spectral channels is better than 150 ms, demonstrating its engineering practical value in hyperspectral data processing.

Key words: linear push-broom oversampling, super-resolution reconstruction, regularized QR decomposition, projection onto convex sets （POCS） method

中图分类号:

TP 391.41

赵俊博, 毛宏霞, 赵慧洁, 张佑堃, 刘畅. QR分解-凸集投影协同超分辨率重建[J]. 系统工程与电子技术, 2026, 48(5): 1474-1480.

Junbo ZHAO, Hongxia MAO, Huijie ZHAO, Youkun ZHANG, Chang LIU. Synergistic super-resolution reconstruction via QR decomposition and POCS[J]. Systems Engineering and Electronics, 2026, 48(5): 1474-1480.

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方法	RRMSE/%	SSIM
插值采样方法	36.09	0.7250
广义逆矩阵方法	21.67	0.7566
完全QR分解方法	14.71	0.8076

方法	RRMSE/%	SSIM
插值采样方法	21.38	0.7924
广义逆矩阵方法	12.64	0.8240
完全QR分解方法	4.24	0.8402

目标过采样率	仿真图像分辨率/m	仿真图像尺寸/像素	重建图像分辨率/m	重建图像尺寸/像素
3	4	43×66	2.4	72×37
2	4	43×53	2.6	65×40
1.5	4	43×44	3.0	58×39

方法	RRMSE/%	SSIM
插值采样方法	32.40	0.7221
广义逆矩阵方法	20.66	0.7349
完全QR分解方法	7.05	0.8064

算法	RRMSE/%	SSIM
插值采样方法	38.14	0.6780
广义逆矩阵方法	30.79	0.6989
完全QR分解方法	10.43	0.7728