【作者】 尹海涛；

【导师】 李树涛；

【作者基本信息】 湖南大学 ， 控制科学与工程， 2012， 博士

【摘要】 稀疏表示是一种新型的图像信息表示理论,能够对图像进行简洁地表示。通过特定的字典,任意图像都可以表示成少数几个原子的线性组合。这些稀疏系数及其对应的原子有效地刻画了图像的内在本质。目前,稀疏表示引起了国内外研究人员广泛关注,并取得了一定的研究成果。但是稀疏表示理论以及相关应用研究仍不完善,一些难点问题亟待解决。因此本论文主要以图像融合和图像复原应用为背景,展开稀疏表示相关理论和应用研究。本论文主要研究工作和创新点如下：1.提出了一种基于联合稀疏模型的多模图像融合算法。该算法在充分考虑不同传感器之间联系的基础上,首先将同一场景的多模图像构成一个信号整体,然后对信号整体进行联合稀疏表示,将其分解成共同稀疏部分和不同稀疏部分,最后通过共同稀疏部分和不同稀疏部分得到融合图像。通过联合稀疏模型获得的共同稀疏部分和不同稀疏部分充分反映出多模图像之间的内在联系,解决了多模图像中互补信息难以分离的问题。2.提出了一种基于稀疏重构的遥感图像融合算法。由于现有遥感卫星无法提供高分辨率多光谱图像,因此已有的基于稀疏表示遥感图像融合方法不能有效地构造高分辨率多光谱图像字典,从而严重制约了此类方法在实际遥感领域中的应用与发展。为了解决这一难题,本文算法采用联合字典学习策略,其中全色图像和低分辨率多光谱图像字典通过样本学习得到,而高分辨率多光谱图像字典从全色图像字典和低分辨率多光谱图像字典中构造出,从而有效地解决了无高分辨率多光谱图像训练样本的难题,极大地提高了算法的实际应用性。此外,本文算法通过联合字典学习策略降低了字典维数、加速了稀疏分解、提高了算法的鲁棒性。3.提出了一种纹理约束稀疏表示模型。该模型充分考虑了图像的复杂纹理特性,采用不同类型的纹理字典对图像中相应的纹理区域进行稀疏表示,解决了单个字典不能对整幅图像中所有纹理信息进行有效稀疏表示的问题。此外,本文还提出了一种基于纹理约束稀疏表示的图像超分辨率算法,通过采用不同的纹理字典对相应的纹理区域进行表示提升了算法对纹理细节的超分辨率复原的性能。4.提出了一种基于稀疏表示的同步图像融合和图像超分辨率算法。为了获得高分辨率融合图像,传统策略需要分别进行图像融合和图像超分辨率,造成扭曲信息的传递并放大。本文算法充分考虑了图像融合和图像超分辨率之间的相似性,并通过稀疏表示将图像融合和图像超分辨率建立一个有机整体,实现了图像融合和图像超分辨率同步完成,有效地解决了低分辨率图像融合问题。5.提出了一种面向群稀疏表示的非凸群稀疏求解模型以及DL-GSGR字典学习算法。群稀疏表示不仅利用了信号的稀疏先验信息,同时还充分考虑了稀疏信号的内在结构,其性能优于传统稀疏表示。针对群稀疏表示求解问题,本文建立了非凸群稀疏求解模型,该模型利用非凸的(?)2,p(0<p<1)范数来度量群稀疏性以及刻画稀疏信号的群结构,详细分析了该模型解的唯一性以及鲁棒性,并提出一种重加权(?)2,1范数优化算法求解该非凸模型,提升群稀疏求解算法的性能。针对群稀疏字典构造问题,本文提出了DL-GSGR算法,该算法利用图正则思想有效地保持了字典中原子之间的几何关系,进而提高字典的表示能力。非凸群稀疏求解模型和DL-GSGR字典学习算法进一步完善了群稀疏表示理论。此外,结合DL-GSGR算法,本文还提出了一种基于群稀疏表示的三维医学图像去噪算法。该去噪算法通过三维处理机制充分利用了三维医学图像中相邻切片图像之间的相似性,并且通过时间正则有效保持相邻切片图像之间的相似性。更多还原

【Abstract】 Sparse representation is a novel image representation theory, which can representate an image concisely. Based on a specific dictionary, any image can be expressed as a linear combination of a few atoms, which can reveal the intrinsic properties of image effectively. Currently, sparse representation has drawn a lot of attentions from the international and domestic researchers, and certain research achievements have been obtained. However, the theory of sparse representation and its applications are imperfect, and some difficulties need to be studied further. Therefore, this thesis mainly investigates the theory of sparse representation and its applications for image fusion and image restoration.The main contributions of this thesis are as follows:1. A multimodal image fusion method based on joint sparse model is proposed. Firstly, the multimodal images for the same scene form a signal ensemble due to the relationship of different sensors. Then, all signals in this ensemble are jointly sparsely represented as common and innovation sparse components. At last, the fused image is generated from the common and innovation sparse components. Specially, the common and innovation sparse components indicate the intrinsic relationship among the multimodal images, which solve the problem of the complementary information separation effectively.2. A remote sensing image fusion method based on sparse reconstruction is proposed. The current method based on sparse representation can not construct the dictionary for high resolution multispectral images (MS) effectively due to the shortage of high resolution MS, which hinders the applications and developments of such method. To solve this problem, the proposed method designs a joint dictionaries learning strategy. In this strategy, the dicitionaries for panchromatic image (PAN) and low resolution MS are learned from training set jointly, and the dictionary for high resolution MS is constructed from the dictionaries for PAN and low resolution MS. The proposed method does not need the high resolution MS training set, which makes the method more practical. In addition, the learned dictionaries can reduce the dimensionality of dictionary, speed up the sparse decomposition, and improve the robustness.3. A texture constrained sparse representation model is proposed. In this model, different texture dictionaries are used to sparsely represent the corresponding texture regions. So it can solve the problem that the single dictionary could not represent all texture information effectively. In addition, this thesis proposes an image super resolution method based on the texture constrained sparse representation model. The sparse representation with corresponding texture dictionaries can improve the performance of super resolution in restorating the texture details.4. A simultaneous image fusion and super resolution method based on sparse representation is proposed. The tradition approaches generate a high-resolution fused image by performing image fusion and super resolution separately, which results in the propagation and magnification of artifacts. Noting that the image fusion and super-resolution have some same foundations, the proposed method makes image fusion and super resolution as an organic whole by sparse representation, which can perform image fusion and super resolution simultaneously, and consequently resolve the problem of low resolution image fusion effectively.5. A non-convex group sparse reconstruction model and the DL-GSGR dictionary learning algorithm for group sparse representation are proposed. Group sparse representation employs the sparse prior information and the intrinsic structure of sparse signal, which surpasses the traditional sparse representation. For the group sparse reconstruction problem, this thesis develops a non-convex group sparse reconstruction model. In this model, the non-convex (?)2,p(0<p<1) norm is used to measure the group sparsity and describe the group structure. The uniqueness and robustness of this model are investigated. Then, a re-weighted (?)2,1norm optimizatipn metod is designed to solve the proposed non-convex model, which can improve the performance of group sparse reconstruction algorithm. For the dictionary construction, this thesis proposes the DL-GSGR which applies the graph regularization to preserve the geometrical structure of atom, and improves the ability of learned dictionay. The non-convex group sparse reconstruction model and the DL-GSGR improve the theory of group sparse representation. In addition, this thesis proposes a3-D medical image denoising algorithm based on the group sparse representation with DL-GSGR. In this denoising algorithm, a3-D processing mechanism is designed which can utilize the correlations among nearby slices effective, and a temporal regularization can preserve the relationship among the nearby slices.更多还原