图像超分辨率重建算法研究
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摘要
图像超分辨率(Super-Resolutin, SR)重建是为了满足人们对高质量图像的需求而产生的一类方法。该方法于20世纪60年代首次提出,目标是使用一幅或多幅低分辨率(Low Resolution, LR)图像中的隐含信息生成一幅或多幅高分辨率(High Resolution, HR)图像。图像超分辨率重建的重要意义在于能够在给定水平的图像采集设备的基础上重建出更高分辨率的图像。
超分辨率重建的主要任务是提高图像的空间分辨率。其基本思想是从输入的低分辨率图像(或图像序列)中寻找高分辨率图像丢失的的高频分量,并进行合理的建模和预测。然而超分辨率重建问题是不适定的,因此需要对该问题的解进行先验约束。可能的约束条件有LR图像之间的时空互补信息,HR图像特征的先验知识以及低分辨率和高分辨率(LR-HR)图像之间的非线性映射关系等。
论文在基于小波变换的金字塔结构下,假设低分辨率图像是小波金字塔的较低层次,采用求解小波金字塔的较高层次的方式获取高分辨率图像。论文应用亚像素位移、梯度以及自相似性等先验约束,使用基于重构和基于学习这两类主流方法分别针对多幅和单幅LR图像开展了超分辨率重建的研究。主要研究工作和创新点如下：
(1)提出了一种基于循环平移的超分辨率(Cycle-Spinning Super-Resolution, CSSR)重建算法。该算法将多幅LR图像经过小波域零填充方法生成多幅HR图像,在充分研究了多幅LR图像之间逆平移运算、平移方向和平移量大小以及取平均运算的基础上,以LR图像之间的亚像素位移作为先验约束,应用图像去噪中的Cycle-Spinning方法改善人工假象对图像分辨率的影响。仿真结果表明,该算法可以有效消除伪吉布斯现象。
(2)提出了一种基于局部李普希兹和梯度先验(Local Lipschitz and Gradient Prior, LLGP)重建算法。该算法将单幅图像分解到小波金字塔结构中,同时计算出不同尺度Lipschitz正则化系数的变化规律,充分考虑了边缘像素沿水平、垂直和对角方向的细节信息,并将其作为HR图像特征的梯度先验,最后使用梯度下降算法获取HR图像。仿真结果表明,该算法可以有效加强图像边缘的锐化效果。
(3)提出了一种基于人工神经网络的自相似性(Self-Similarity by Artificial Neural Network, SS-ANN)重建算法。该算法首先通过对单幅图像进行小波变换,建立包含不同尺度图像的金字塔结构;其次,将这种相同和不同尺度上LR-HR图像块之间细节信息的相似性作为先验约束对人工神经网络(Artificial Neural Network, ANN)进行训练；最后从训练好的ANN模型中预测因降质丢失的高频分量,再经过小波逆变换获得HR图像的初始估计,并应用误差函数对该初始估计进行约束。仿真结果表明,该算法可以有效逼近真实的HR图像。
综上所述,论文在基于小波变换的金字塔结构下,对LR图像之间的时空互补信息、HR图像特征的先验知识和LR-HR图像之间的非线性映射关系这三种先验约束分别进行了研究,同时将Cycle-Spinning、Lipschitz正则化和ANN等方法应用于问题的建模和求解中,提出了新的超分辨率重建算法,取得了较有价值的研究成果。
Super-resolution image reconstruction is a kind of method that satisfies the demand for high quality images. First proposed in the1960s, its goal is to reconstruct one or a series of high resolution (HR) image(s) by exploiting hidden information from one or a sequence of low resolution (LR) original image(s). The significance of super-resolution image reconstruction lies in its ability to reconstruct higher resolution images on top of image acquisition devices with inherently restricted resolution capacity.
The main task of super-resolution image reconstruction is to elevate the spatial resolution of images. The basic idea is to find the high-frequency constituents in the high resolution image that was lost from one or a sequence of low resolution image(s) and then perform reasonable modeling and predicting. However, super-resolution image reconstruction is an ill-posed problem, so prior constraints are required to be imposed on its solution. Possible constraints include time-space complementary information among LRs, prior knowledge on the characteristics of the HRs and non-linear mapping relationships between LRs and HRs.
Rested on the wavelet transform based pyramid framework, the thesis assumes that the LR images were located at the lower level of the pyramid and reconstructs HR images by solving the higher levels of the wavelet pyramid. The research is conducted on two mainstream approaches, reconstruction based and learning based, with sub-pixel shifts, gradients and self-similarity as prior constraints. The major research work and contributions are listed as follows:
(1) Propose a reconstruction based algorithm CSSR (Cycle-Spinning Super-Resolution). CSSR is based on a thorough investigation on the inverse translation operation, the translation direction and amount along with the averaging among multiple LRs, and applies Cycle-Spinning in image denoising to improve the image resolution by eliminating the impacts by artifacts, taking sub-pixel shift as the prior constraint. Simulation results indicate that CSSR algorithm could eliminate Pseudo-Gibbs phenomenon effectively.
(2) Propose a learning based algorithm LLGP (Local Lipschitz and Gradient Prior). LLGP incorporates the way that Lipschitz regularization coefficients varies w.r.t different scales into the wavelet pyramid structure first, then takes gradients from a full analysis of detailed information of the edge pixels along horizontal, vertical and diagonal directions as the prior of image characteristics, and finally reconstructs HR by means of gradient descent method. Simulation results show that LLGP algorithm can remarkably enhance the sharpness at edge pixels.
(3) Propose a learning based algorithm SS-ANN (Self-Similarity by Artificial Neural Network). SS-ANN constructs a pyramid structure containing images of different scales by wavelet transform of a single image first, then trains ANN taking the similarity of the detailed information among LR-HR image patches with the same and different scales as a prior, subsequently predicts high-frequency constituents lost by quality degrading from the ANN model, figures initial estimation of HR by inverse wavelet transform as the next step, and finally applies error function to constrain the initial estimation. Simulation experiments demonstrate that SS-ANN algorithm can approximate the real HR image much effectively.
To sum up, based on the pyramid framework of wavelet transform, the thesis has conducted researches on three kinds of priors:time-space complementary information among LRs, characteristics of HRs and the non-linear mapping relationship between LRs and HRs, applied Cycle-Spinning, Lipschitz regularization and ANN to the modeling and resolving of super-resolution image reconstruction, and proposed novel algorithms whose effectiveness have been well demonstrated by simulation experiments.
超分辨率重建的主要任务是提高图像的空间分辨率。其基本思想是从输入的低分辨率图像(或图像序列)中寻找高分辨率图像丢失的的高频分量,并进行合理的建模和预测。然而超分辨率重建问题是不适定的,因此需要对该问题的解进行先验约束。可能的约束条件有LR图像之间的时空互补信息,HR图像特征的先验知识以及低分辨率和高分辨率(LR-HR)图像之间的非线性映射关系等。
论文在基于小波变换的金字塔结构下,假设低分辨率图像是小波金字塔的较低层次,采用求解小波金字塔的较高层次的方式获取高分辨率图像。论文应用亚像素位移、梯度以及自相似性等先验约束,使用基于重构和基于学习这两类主流方法分别针对多幅和单幅LR图像开展了超分辨率重建的研究。主要研究工作和创新点如下：
(1)提出了一种基于循环平移的超分辨率(Cycle-Spinning Super-Resolution, CSSR)重建算法。该算法将多幅LR图像经过小波域零填充方法生成多幅HR图像,在充分研究了多幅LR图像之间逆平移运算、平移方向和平移量大小以及取平均运算的基础上,以LR图像之间的亚像素位移作为先验约束,应用图像去噪中的Cycle-Spinning方法改善人工假象对图像分辨率的影响。仿真结果表明,该算法可以有效消除伪吉布斯现象。
(2)提出了一种基于局部李普希兹和梯度先验(Local Lipschitz and Gradient Prior, LLGP)重建算法。该算法将单幅图像分解到小波金字塔结构中,同时计算出不同尺度Lipschitz正则化系数的变化规律,充分考虑了边缘像素沿水平、垂直和对角方向的细节信息,并将其作为HR图像特征的梯度先验,最后使用梯度下降算法获取HR图像。仿真结果表明,该算法可以有效加强图像边缘的锐化效果。
(3)提出了一种基于人工神经网络的自相似性(Self-Similarity by Artificial Neural Network, SS-ANN)重建算法。该算法首先通过对单幅图像进行小波变换,建立包含不同尺度图像的金字塔结构;其次,将这种相同和不同尺度上LR-HR图像块之间细节信息的相似性作为先验约束对人工神经网络(Artificial Neural Network, ANN)进行训练；最后从训练好的ANN模型中预测因降质丢失的高频分量,再经过小波逆变换获得HR图像的初始估计,并应用误差函数对该初始估计进行约束。仿真结果表明,该算法可以有效逼近真实的HR图像。
综上所述,论文在基于小波变换的金字塔结构下,对LR图像之间的时空互补信息、HR图像特征的先验知识和LR-HR图像之间的非线性映射关系这三种先验约束分别进行了研究,同时将Cycle-Spinning、Lipschitz正则化和ANN等方法应用于问题的建模和求解中,提出了新的超分辨率重建算法,取得了较有价值的研究成果。
Super-resolution image reconstruction is a kind of method that satisfies the demand for high quality images. First proposed in the1960s, its goal is to reconstruct one or a series of high resolution (HR) image(s) by exploiting hidden information from one or a sequence of low resolution (LR) original image(s). The significance of super-resolution image reconstruction lies in its ability to reconstruct higher resolution images on top of image acquisition devices with inherently restricted resolution capacity.
The main task of super-resolution image reconstruction is to elevate the spatial resolution of images. The basic idea is to find the high-frequency constituents in the high resolution image that was lost from one or a sequence of low resolution image(s) and then perform reasonable modeling and predicting. However, super-resolution image reconstruction is an ill-posed problem, so prior constraints are required to be imposed on its solution. Possible constraints include time-space complementary information among LRs, prior knowledge on the characteristics of the HRs and non-linear mapping relationships between LRs and HRs.
Rested on the wavelet transform based pyramid framework, the thesis assumes that the LR images were located at the lower level of the pyramid and reconstructs HR images by solving the higher levels of the wavelet pyramid. The research is conducted on two mainstream approaches, reconstruction based and learning based, with sub-pixel shifts, gradients and self-similarity as prior constraints. The major research work and contributions are listed as follows:
(1) Propose a reconstruction based algorithm CSSR (Cycle-Spinning Super-Resolution). CSSR is based on a thorough investigation on the inverse translation operation, the translation direction and amount along with the averaging among multiple LRs, and applies Cycle-Spinning in image denoising to improve the image resolution by eliminating the impacts by artifacts, taking sub-pixel shift as the prior constraint. Simulation results indicate that CSSR algorithm could eliminate Pseudo-Gibbs phenomenon effectively.
(2) Propose a learning based algorithm LLGP (Local Lipschitz and Gradient Prior). LLGP incorporates the way that Lipschitz regularization coefficients varies w.r.t different scales into the wavelet pyramid structure first, then takes gradients from a full analysis of detailed information of the edge pixels along horizontal, vertical and diagonal directions as the prior of image characteristics, and finally reconstructs HR by means of gradient descent method. Simulation results show that LLGP algorithm can remarkably enhance the sharpness at edge pixels.
(3) Propose a learning based algorithm SS-ANN (Self-Similarity by Artificial Neural Network). SS-ANN constructs a pyramid structure containing images of different scales by wavelet transform of a single image first, then trains ANN taking the similarity of the detailed information among LR-HR image patches with the same and different scales as a prior, subsequently predicts high-frequency constituents lost by quality degrading from the ANN model, figures initial estimation of HR by inverse wavelet transform as the next step, and finally applies error function to constrain the initial estimation. Simulation experiments demonstrate that SS-ANN algorithm can approximate the real HR image much effectively.
To sum up, based on the pyramid framework of wavelet transform, the thesis has conducted researches on three kinds of priors:time-space complementary information among LRs, characteristics of HRs and the non-linear mapping relationship between LRs and HRs, applied Cycle-Spinning, Lipschitz regularization and ANN to the modeling and resolving of super-resolution image reconstruction, and proposed novel algorithms whose effectiveness have been well demonstrated by simulation experiments.
引文
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