摘要
超分辨率图像恢复是近年来才出现的图像处理方法，该方法通过对图像序列作图像运动估计、图像信息融合、去模糊和去噪声等，从低分辨图像序列的多张图像中恢复细节更精细的高分辨率图像，是一种既经济又容易实现的图像分辨率提高方法，可用于提高遥感和医学等图像的分辨率。本文从单独考虑超分辨率图像内插，同时考虑图像模糊估计与高分辨率图像盲恢复，以及同时考虑图像运动、模糊估计与高分辨率图像盲恢复等三种不同处理方式，对超分辨率图像恢复中的方法进行了研究。
在仅考虑超分辨率图像内插方面，改进了现有超分辨率图像小波内插。首先指出现有超分辨率图像小波内插的不足在于它采用的是缺乏位移不变性和方向可选择性的二维实离散小波变换(DWT，discrete wavelet transformation)，使得该方法恢复的高分辨率图像中容易出现“振铃效应”，在恢复细节时可选方向少。本文提出一种改进的超分辨率图像小波内插，采用具有位移不变性和更多方向可选性的二元树复小波变换(DT CWT，dual tree complex transforrnation)，代替超分辨率图像小波内插中的DWT，使超分辨率图像内插可选的细节方向增多，恢复图像中的“振铃效应”也明显减少。给出了超分辨率图像DT CWT内插的计算方法。用人工低分辨率图像序列进行实验，实验结果表明了本文改进方法的有效性。
在同时考虑图像模糊估计和高分辨率图像恢复方面，改进了现有线性正则有参超分辨率图像盲恢复在正则处理上的不足。由于现有线性正则有参超分辨率图像盲恢复在线性的Tikhonov正则中，采用的是线性位移不变的正则参数和高通低不阻的恒定正则算子，导致该方法不能在高分辨率恢复图像中较好地保留图像边缘细节。本文提出线性自适应正则有参超分辨率图像盲恢复，在Tikhonov正则中引入高通低阻的Laplacian正则算子，用反映图像局部光滑特征的梯度信息对正则参数进行局部加权，使正则参数能随图像光滑特征自适应地改变大小，从而使高分辨率恢复图像中的边缘细节能更好地得到保留。给出了线性自适应正则有参超分辨率图像盲恢复的近似求解和计算步骤。在人工低分辨率图像序列上进行实验，实验结果表明了本文正则改进方法的有效性。
在同时考虑模糊估计和高分辨率图像恢复方面，还改进了现有线性正则有参超分辨率图像盲恢复在图像模型边界处理上的不足。由于现有线性正则有参超分辨率图像盲恢复基于的是静态的和零边界条件的图像模型，使得该方法在上述边界条件不满足时，容易在高分辨率恢复图像的边框处产生“振铃效应”。提出线性正则有参超分辨率图像盲恢复方法的边界改进方法，即：用Neumann边界构
Super Resolution image restoration (SR) is a newcome image processing method that extracting higher resolution images containing more details from an image sequence of lower resolution, by image process such as motion estimation, deblurring and denoising. Currently SR is one active image processing field, in which the obtained algorithms can be used to improve image resolution in remote sensing and medical applications. In this paper, algorithms in three kinds of SR processing manner are studied, that are: only considering SR interpolation, considering together blurring estimation and high-resolution image restoration, and simultaneously considering image motion, blurring estimation and high-resolution image restoration.
When only considering SR interpolation, some improvement to the existing wavelet-based SR interpolation is proposed. It is pointed out that because of the adopted 2-D real Discrete Wavelet Transformation(DWT) lacking of shift-invariance and direction selectivity, thus in the restored high resolution image obtained by Wavelet-based SR interpolation, there will appears some undesired Ringing Effects, and only few directions of details can be selected to restore by wavelet-based SR interpolation. Dual-Tree Complex Wavelet (DT CWT), which has nearly shift-invariance and direction selectivity with limited data redundancy, is proposed to replace 2-D real DWT in wavelet-based SR interpolation, thus not only make more selectivity of detail directions, but can also reduce the Ringing Effects in the restored high resolution image. Related computation steps are given. Tests results on synthetical lower resolution image sequences are also presented to show the validation of the proposed SR interpolation based on DT CWT.
When considering image blurring estimation and high resolution image restoration together, improvements are proposed to the regularization method of the existing linear regularized and parametric SR blind restoration (LR PBSR). It is analyzed that because in the existing LR PBSR the adapted Tikhonov regularization is linear shift-invariance, and the adapted identity regularization operation is high-pass and low-not-stop, thus over smoothing will be induced into edge areas of the restored image which will decimate the restored image. In the same linear Tikhonov regularization frame, By adding into the regularization term a high-pass and low-stop Laplacian regularization operator and a weight matrix defined by the gradient vector magnitude which representing the local smoothing features, an local adopted linear regularization and parametric blind SR is realized, which make the regularization
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