图像压缩感知重建算法研究
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摘要
压缩感知理论是一种新颖的采样理论,具有在信号采样率非常低的情况下精确重建信号的特点,近年来吸引了相关领域学者的广泛关注和研究热情。压缩感知重建算法作为压缩感知理论的核心内容之一,直接关系着压缩感知理论在实际应用中的成败。自压缩感知理论提出以来,如何设计出算法复杂度低、重建信号质量高的压缩感知重建算法以精确重建出信号特别是大尺度图像信号,一直是研究的重点课题。本文正是在这一背景下,以图像信号的压缩感知重建算法为研究对象,对其进行了深入广泛的研究,致力于寻找高效、鲁棒的压缩感知重建算法。本文工作的主要贡献和创新总结如下：
1.在深入研究匹配追踪类算法及其原子选择准则的基础上,针对正交匹配追踪算法在每次迭代中不能选取出最优原子的问题,提出了基于优化正交匹配追踪的压缩感知重建算法,从理论上分析了该算法原子选择的最优性。通过在不同测量矩阵下得到的仿真实验结果,证明了该算法的有效性。
2.针对现有方向追踪算法重建精度和算法效率上的不足,提出了基于谱投影梯度追踪的压缩感知重建算法。该算法采用方向追踪法框架,运用谱投影梯度方法计算更新方向和步长,引入非单调线性搜索策略使算法避免收敛至局部最优解,并且通过设定合适的阈值参数可以取得重建精度和算法效率之间的平衡。仿真实验结果证明了该算法具有较高的重建精度,并且算法效率明显提高。
3.针对多数现有算法基于单观测向量模型,在处理图像信号时将其转换为维信号,造成算法效率低和重建精度不理想的问题,提出了基于多观测向量模型和稀疏贝叶斯学习的压缩感知重建算法。该算法采用压缩感知理论框架下与图像信号相适应的多观测向量模型,通过同时处理观测矩阵的每一列直接求得加权系数矩阵,从而快速重建图像。稀疏贝叶斯学习算法的应用,使得加权系数矩阵具有很好的稀疏性,保证了重建图像的质量。通过仿真实验,证明了该算法完成图像重建所需时间明显缩短,并且重建图像精度更高。
4.现有的用于图像信号的多尺度压缩感知方案,只对图像信号被采样的小波系数进行重建,不用于采样的小波系数则直接置零,造成图像边缘粗糙,影响了图像重建质量。针对该问题,提出了一种改进的多尺度压缩感知方案。新方案在原方案得到的重建图像基础上,通过轮廓波变换进行图像插值,估计出原来被置零的小波系数,从而改善了图像的重建质量。仿真实验结果表明,该方案重建出的图像克服了原方案存在的马赛克效应,重建图像质量更高。
Compressed sensing is a novel sampling theory. This theory shows that a small number of random projections of a compressible signal contain enough information for exact reconstruction. It has gained much attention in the past few years due to its promising practical potentials. As one of the crucial issues, the reconstruction algorithm plays a key role in the application of compressed sensing and affects its practical usage. Since the compressed sensing theory was presented, how to design a reconstruction algorithm with low complexity and high reconstruction accuracy to reconstruct signal, especially the large scale image signal, has been a hot study. Under this background, the dissertation has deeply studied the compressed sensing reconstruction algorithms for image in order to find robust and effective reconstruction algorithms. The main contributions and innovations of the dissertation are as follows.
1. The traditional class of matching pursuit algorithm is deeply studied and its atom selection strategy is analyzed. As the orthogonal matching pursuit algorithm can not select the best atom in each iteration, an optimized orthogonal matching pursuit algorithm for compressed sensing reconstruction is proposed. The theory analysis of its atom selection strategy is presented. The validity of the proposed algorithm is proved by the experiments under different measurement matrixes.
2. In order to improve the reconstruction accuracy and efficiency of the directional pursuit algorithm, a compressed sensing reconstruction algorithm based on spectral projected gradient pursuit is proposed. Directional pursuit frame is adopted by this algorithm. The update direction and step length are computed by spectral projected gradient method. Local optimum point is avoided by adopting the nonmonotone line search strategy. The balance between reconstruction accuracy and efficiency of the algorithm can be achieved by setting an appropriate threshold parameter. The experimental results show that this algorithm has better reconstruction accuracy and efficiency.
3. Most existing compressed sensing reconstruction algorithms are based on single measurement vector. When processing image signal, the efficiency of these algorithms is low and the quality of the reconstructed image is not good enough, because the image is treated as one dimension signal. A reconstruction algorithm based on multiple measurement vectors and sparse Bayesian learning is proposed. By using the multiple measurement vectors model that suits image processing in compressed sensing, the image can be reconstructed quickly because the weighting coefficient matrix can be got directly by processing each column of the measurement matrix simultaneously. The sparse Bayesian learning algorithm guarantees the sparsity of the weighting coefficient matrix. The experimental results show that the proposed algorithm has better reconstruction accuracy and the efficiency is improved obviously.
4. According to the existing multiscale compressed sensing scheme, only a few of wavelet coefficients are sampled and the others are set to zero, which results in the coarse edges of the reconstruction images and low reconstruction accuracy. In order to overcome this conundrum, an improved multiscale compressed sensing scheme which interpolates the image reconstructed by multiscale compressed sensing scheme with contourlet transform is proposed. The reconstruction accuracy of the new scheme is improved by estimating the unsampled wavelet coefficients and keeping the sampled unchanged. The experimental results show that the proposed scheme overcomes the mosaic effect and has better reconstruction accuracy than the existing scheme.
1.在深入研究匹配追踪类算法及其原子选择准则的基础上,针对正交匹配追踪算法在每次迭代中不能选取出最优原子的问题,提出了基于优化正交匹配追踪的压缩感知重建算法,从理论上分析了该算法原子选择的最优性。通过在不同测量矩阵下得到的仿真实验结果,证明了该算法的有效性。
2.针对现有方向追踪算法重建精度和算法效率上的不足,提出了基于谱投影梯度追踪的压缩感知重建算法。该算法采用方向追踪法框架,运用谱投影梯度方法计算更新方向和步长,引入非单调线性搜索策略使算法避免收敛至局部最优解,并且通过设定合适的阈值参数可以取得重建精度和算法效率之间的平衡。仿真实验结果证明了该算法具有较高的重建精度,并且算法效率明显提高。
3.针对多数现有算法基于单观测向量模型,在处理图像信号时将其转换为维信号,造成算法效率低和重建精度不理想的问题,提出了基于多观测向量模型和稀疏贝叶斯学习的压缩感知重建算法。该算法采用压缩感知理论框架下与图像信号相适应的多观测向量模型,通过同时处理观测矩阵的每一列直接求得加权系数矩阵,从而快速重建图像。稀疏贝叶斯学习算法的应用,使得加权系数矩阵具有很好的稀疏性,保证了重建图像的质量。通过仿真实验,证明了该算法完成图像重建所需时间明显缩短,并且重建图像精度更高。
4.现有的用于图像信号的多尺度压缩感知方案,只对图像信号被采样的小波系数进行重建,不用于采样的小波系数则直接置零,造成图像边缘粗糙,影响了图像重建质量。针对该问题,提出了一种改进的多尺度压缩感知方案。新方案在原方案得到的重建图像基础上,通过轮廓波变换进行图像插值,估计出原来被置零的小波系数,从而改善了图像的重建质量。仿真实验结果表明,该方案重建出的图像克服了原方案存在的马赛克效应,重建图像质量更高。
Compressed sensing is a novel sampling theory. This theory shows that a small number of random projections of a compressible signal contain enough information for exact reconstruction. It has gained much attention in the past few years due to its promising practical potentials. As one of the crucial issues, the reconstruction algorithm plays a key role in the application of compressed sensing and affects its practical usage. Since the compressed sensing theory was presented, how to design a reconstruction algorithm with low complexity and high reconstruction accuracy to reconstruct signal, especially the large scale image signal, has been a hot study. Under this background, the dissertation has deeply studied the compressed sensing reconstruction algorithms for image in order to find robust and effective reconstruction algorithms. The main contributions and innovations of the dissertation are as follows.
1. The traditional class of matching pursuit algorithm is deeply studied and its atom selection strategy is analyzed. As the orthogonal matching pursuit algorithm can not select the best atom in each iteration, an optimized orthogonal matching pursuit algorithm for compressed sensing reconstruction is proposed. The theory analysis of its atom selection strategy is presented. The validity of the proposed algorithm is proved by the experiments under different measurement matrixes.
2. In order to improve the reconstruction accuracy and efficiency of the directional pursuit algorithm, a compressed sensing reconstruction algorithm based on spectral projected gradient pursuit is proposed. Directional pursuit frame is adopted by this algorithm. The update direction and step length are computed by spectral projected gradient method. Local optimum point is avoided by adopting the nonmonotone line search strategy. The balance between reconstruction accuracy and efficiency of the algorithm can be achieved by setting an appropriate threshold parameter. The experimental results show that this algorithm has better reconstruction accuracy and efficiency.
3. Most existing compressed sensing reconstruction algorithms are based on single measurement vector. When processing image signal, the efficiency of these algorithms is low and the quality of the reconstructed image is not good enough, because the image is treated as one dimension signal. A reconstruction algorithm based on multiple measurement vectors and sparse Bayesian learning is proposed. By using the multiple measurement vectors model that suits image processing in compressed sensing, the image can be reconstructed quickly because the weighting coefficient matrix can be got directly by processing each column of the measurement matrix simultaneously. The sparse Bayesian learning algorithm guarantees the sparsity of the weighting coefficient matrix. The experimental results show that the proposed algorithm has better reconstruction accuracy and the efficiency is improved obviously.
4. According to the existing multiscale compressed sensing scheme, only a few of wavelet coefficients are sampled and the others are set to zero, which results in the coarse edges of the reconstruction images and low reconstruction accuracy. In order to overcome this conundrum, an improved multiscale compressed sensing scheme which interpolates the image reconstructed by multiscale compressed sensing scheme with contourlet transform is proposed. The reconstruction accuracy of the new scheme is improved by estimating the unsampled wavelet coefficients and keeping the sampled unchanged. The experimental results show that the proposed scheme overcomes the mosaic effect and has better reconstruction accuracy than the existing scheme.
引文
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