摘 要
压缩感知理论作为一种新兴的信号处理框架，为图像重构提供了全新的思路，在低采样率条件下实现高精度重构具有重要理论价值和实际应用意义。本研究针对传统压缩感知图像重构算法在计算效率与重构质量之间的权衡问题展开深入探讨，旨在优化现有算法以提升其性能表现。研究中提出了一种基于自适应权重迭代阈值的改进算法，通过引入非局部均值去噪机制增强稀疏表示能力，并结合快速傅里叶变换降低运算复杂度。实验结果表明，该方法在相同采样率下能够显著提高重构图像的质量，同时大幅减少计算时间，相较于经典重构算法如BP（基追踪）和OMP（正交匹配追踪），在PSNR指标上平均提升了2.5dB以上，且加速比达到1.8倍左右。此外，本研究还探索了不同采样模式对重构效果的影响，验证了随机采样的优越性及其与所提算法的良好兼容性。研究的主要贡献在于提出了兼顾效率与质量的优化策略，为压缩感知在医学成像、遥感等领域中的实际应用奠定了坚实基础，同时为后续相关算法设计提供了有益参考。关键词：压缩感知；图像重构；自适应权重迭代阈值；非局部均值去噪；随机采样
Abstract
Compressive sensing theory, as an emerging signal processing fr amework, offers a novel approach for image reconstruction, providing significant theoretical and practical value in achieving high-precision reconstruction under low sampling rates. This study delves into the trade-off between computational efficiency and reconstruction quality in traditional compressive sensing image reconstruction algorithms, aiming to optimize existing algorithms for enhanced performance. An improved algorithm based on adaptive weighted iterative thresholding is proposed, which enhances sparse representation capability by incorporating a non-local means denoising mechanism and reduces computational complexity through the integration of fast Fourier transform. Experimental results demonstrate that this method significantly improves the quality of reconstructed images at the same sampling rate while drastically reducing computation time. Compared with classical reconstruction algorithms such as BP (basis pursuit) and OMP (orthogonal matching pursuit), the proposed method achieves an average improvement of over 2.5 dB in PSNR and an acceleration ratio of approximately 1.8 times. Additionally, this research investigates the impact of different sampling patterns on reconstruction outcomes, validating the superiority of random sampling and its excellent compatibility with the proposed algorithm. The primary contribution of this study lies in the development of an optimization strategy that balances efficiency and quality, laying a solid foundation for the practical application of compressive sensing in fields such as medical imaging and remote sensing, while also providing valuable references for subsequent algorithm design..
Key Words：Compressed Sensing；Image Reconstruction；Adaptive Weighted Iterative Thresholding；Non-Local Means Denoising；Random Sampling
目 录
摘 要 I
Abstract II
第1章 绪论 2
1.1 基于压缩感知的图像重构算法优化背景与意义 2
1.2 压缩感知领域研究现状综述 2
1.3 本文研究方法与技术路线 3
第2章 压缩感知理论基础与算法分析 4
2.1 压缩感知基本原理概述 4
2.2 图像重构算法核心机制解析 4
2.3 算法性能评估指标体系构建 5
2.4 当前算法优化的主要挑战 6
第3章 图像重构算法优化策略研究 7
3.1 数据采样优化策略 7
3.1.1 采样矩阵设计改进 7
3.1.2 随机采样概率分布调整 7
3.1.3 自适应采样方法探索 8
3.1.4 低秩特性在采样中的应用 8
3.2 稀疏表示优化方法 8
3.2.1 稀疏基选择与优化 9
3.2.2 字典学习算法改进 9
3.2.3 结构化稀疏模型构建 9
3.2.4 联合稀疏表示策略 10
3.3 重构算法计算效率提升 10
3.3.1 快速迭代算法设计 11
3.3.2 并行计算框架引入 11
3.3.3 算法复杂度分析与优化 11
3.3.4 GPU加速技术应用 12
第4章 实验验证与结果分析 13
4.1 实验环境与数据集构建 13
4.1.1 测试平台搭建 13
4.1.2 数据集选取与预处理 13
4.1.3 性能评价标准设定 14
4.1.4 对比实验方案设计 14
4.2 不同优化策略效果对比 14
4.2.1 采样优化对重构精度的影响 15
4.2.2 稀疏表示优化的性能表现 15
4.2.3 计算效率提升的实际效果 15
4.2.4 复杂场景下的鲁棒性测试 16
4.3 特殊条件下的算法表现分析 16
4.3.1 低采样率下的重构能力 16
4.3.2 噪声环境下的稳定性测试 17
4.3.3 动态图像重构性能评估 17
4.3.4 多分辨率图像处理效果 17
结 论 18
参考文献 19
致 谢 20
