压缩感知在图像处理中的应用研究
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摘要
随着压缩感知理论研究工作的深入,压缩感知在信号和图像处理领域已引起众多研究者的关注。理论已经证明自然图像本身具有稀疏的表示特性,符合人类所接触的很多信号和图像的处理。随着稀疏表示算法的不断完善,特别是学习字典理论提出之后,近年来,压缩感知理论已被大量应用到信号和图像处理的各个领域。
本文基于压缩感知理论,围绕图像识别和图像超分辨率重建问题,重点研究了如何构造更高鲁棒性和更少计算复杂度的分类识别算法,以及如何构造冗余字典更有效地重建超分辨率图像。主要工作如下:
1)研究基于压缩感知的图像识别算法,阐述基于稀疏表示的SRC(Sparse Representation-based Classification)方法理论框架,由于SRC方法利用L1范数最小化算法求解稀疏表示系数在计算复杂度上过高,采用计算复杂度较低的OMP(Orthogonal Matching Pursuit,正交匹配追踪)算法对SRC方法进行改进。
2)针对SRC方法在低维情况下识别率较低,提出基于类别信息的SRC识别方法,人脸识别和空间目标识别实验表明,该方法在低维情况下提高了识别率且具有较强的抗噪声能力。
3)研究基于稀疏表示的图像重建算法,将其应用到YCbCr、RGB彩色图像模型来进行超分辨率重建,并与经典的如最近二次插值、三次插值、邻域插值和小波与局部适应插值等方法进行分析比较,实验结果表明相对于经典方法,基于稀疏表示的图像重建算法对灰度和彩色图像的重建效果优势明显。
The further research of the Compressed Sensing(CS) theory draws many researchers attention in signal and image processing area. Natural images are proven has the feature of Sparse Representation, which accord with much signal and image processing work people usually contact. As the improving of Sparse Representation algorithms, especially after put forward of learning dictionary theory, the CS theory has been applied to signal and image processing fields.
Based on the CS theory, and centered on image recognition and super resolution reconstruction of images, this thesis focuses on how to construct a classification recognition algorithm with high robust and low computational complexity, and how to construct overcomplete dictionary to build super-resolution image more effectively.
The main works are described as follows:
1) Based on Sparse Representation, SRC (Sparse Representation-based Classification) theory framework is stated in details. Due to the high computational complexity in using the L1 norm minimize algorithm to get the Sparse Representation coefficient of SRC methods. We propose an OMP (Orthogonal Matching Pursuit) algorithm with lower computational complexity to improve SRC method.
2) For the problem of the low recognition rate of SRC method in under low dimensional case, a new SRC recognition method based on the categories information is presented. Face recognition and space target recognition experiment shows that this method improves recognition rate under low dimension case and has strong anti-noise ability.
3) Based on Sparse Representation, image reconstruction algorithm is stated to reconstruct super-resolution by using YCbCr or RGB color image model, and also contrasted to traditional methods such as nearest neighbor interpolation, wavelet interpolation and etc, and the experience result shows that image reconstruction algorithm based on Sparse Representation has obvious advantages compared with traditional method on reconstruction of grey level and color images.
本文基于压缩感知理论,围绕图像识别和图像超分辨率重建问题,重点研究了如何构造更高鲁棒性和更少计算复杂度的分类识别算法,以及如何构造冗余字典更有效地重建超分辨率图像。主要工作如下:
1)研究基于压缩感知的图像识别算法,阐述基于稀疏表示的SRC(Sparse Representation-based Classification)方法理论框架,由于SRC方法利用L1范数最小化算法求解稀疏表示系数在计算复杂度上过高,采用计算复杂度较低的OMP(Orthogonal Matching Pursuit,正交匹配追踪)算法对SRC方法进行改进。
2)针对SRC方法在低维情况下识别率较低,提出基于类别信息的SRC识别方法,人脸识别和空间目标识别实验表明,该方法在低维情况下提高了识别率且具有较强的抗噪声能力。
3)研究基于稀疏表示的图像重建算法,将其应用到YCbCr、RGB彩色图像模型来进行超分辨率重建,并与经典的如最近二次插值、三次插值、邻域插值和小波与局部适应插值等方法进行分析比较,实验结果表明相对于经典方法,基于稀疏表示的图像重建算法对灰度和彩色图像的重建效果优势明显。
The further research of the Compressed Sensing(CS) theory draws many researchers attention in signal and image processing area. Natural images are proven has the feature of Sparse Representation, which accord with much signal and image processing work people usually contact. As the improving of Sparse Representation algorithms, especially after put forward of learning dictionary theory, the CS theory has been applied to signal and image processing fields.
Based on the CS theory, and centered on image recognition and super resolution reconstruction of images, this thesis focuses on how to construct a classification recognition algorithm with high robust and low computational complexity, and how to construct overcomplete dictionary to build super-resolution image more effectively.
The main works are described as follows:
1) Based on Sparse Representation, SRC (Sparse Representation-based Classification) theory framework is stated in details. Due to the high computational complexity in using the L1 norm minimize algorithm to get the Sparse Representation coefficient of SRC methods. We propose an OMP (Orthogonal Matching Pursuit) algorithm with lower computational complexity to improve SRC method.
2) For the problem of the low recognition rate of SRC method in under low dimensional case, a new SRC recognition method based on the categories information is presented. Face recognition and space target recognition experiment shows that this method improves recognition rate under low dimension case and has strong anti-noise ability.
3) Based on Sparse Representation, image reconstruction algorithm is stated to reconstruct super-resolution by using YCbCr or RGB color image model, and also contrasted to traditional methods such as nearest neighbor interpolation, wavelet interpolation and etc, and the experience result shows that image reconstruction algorithm based on Sparse Representation has obvious advantages compared with traditional method on reconstruction of grey level and color images.
引文
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