Researchers usually use several assumptions when they tackle the image deblurring problem. In particular, it is usually assumed that the blur is known exactly, and that the true image scene outside the field of view is approximated well by periodic boundary conditions. These assumptions are certainly not true in most realistic situations.;In this thesis we develop a new method to derive adaptive synthetic boundary conditions directly from the blurred images. Compared with classical boundary conditions, our approach gives better deblurring results, especially for motion blurred images. To speed up the deblurring algorithms, we also develop a new regularized DCT preconditioner.;We have written two new software packages to facilitate research in image deblurring. The first one PYRET is a serial CPU implementation in Python. With the object-oriented paradigm, we implement numerical algorithms for the general linear problem, and then specialize them for deblurring problems with a new matrix class. A web user interface for PYRET is also provided.;The second software package PARRET is a parallel implementation on NVIDIA CUDA GPU architecture. GPUs provide an economical way to obtain parallel processing power. On a consumer laptop equipped with a GPU, we can attain order of magnitude speedup with PARRET.;Finally, we consider a blind deconvolution problem in which the involved atmospheric blurs are not known in advance. We first reduce the number of variables using a variable projection technique, then solve the reduced problem by the Gauss-Newton algorithm. With careful mathematical manipulation, the Jacobian matrix is decomposed into a series of diagonal and Fourier matrices for inexpensive multiplication. To further improve the deblurring quality, we use more than one blurred image from the same object. We use a new decoupling approach for the sparsity of the Jacobian matrix in this multi-frame case. Experiments show that the deblurring result improves when more images are used.
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机译：研究人员在解决图像去模糊问题时通常会使用几种假设。特别地，通常假设模糊是精确已知的，并且视场外的真实图像场景可以通过周期性边界条件很好地近似。这些假设在大多数现实情况下肯定是不正确的。；本文提出了一种直接从模糊图像中导出自适应合成边界条件的新方法。与经典边界条件相比，我们的方法可以提供更好的去模糊效果，尤其是对于运动模糊图像。为了加快去模糊算法，我们还开发了一种新的正则化DCT预调节器。我们编写了两个新的软件包，以方便图像去模糊的研究。第一个PYRET是Python中的串行CPU实现。使用面向对象的范例，我们为一般的线性问题实现了数值算法，然后将它们专用于使用新的矩阵类对问题进行模糊处理。还提供了PYRET的Web用户界面。第二个软件包PARRET是在NVIDIA CUDA GPU架构上的并行实现。 GPU提供了一种经济的方式来获得并行处理能力。在配备GPU的消费类笔记本电脑上，我们可以使用PARRET达到数量级的加速；最后，我们考虑一个盲反卷积问题，其中事先不了解所涉及的大气模糊。我们首先使用变量投影技术减少变量的数量，然后通过高斯-牛顿算法解决减少的问题。通过仔细的数学处理，雅可比矩阵被分解为一系列对角和傅立叶矩阵，从而实现了廉价的乘法运算。为了进一步提高去模糊质量，我们使用了来自同一物体的多个模糊图像。在这种多帧情况下，我们对雅可比矩阵的稀疏性使用了一种新的去耦方法。实验表明，当使用更多图像时，去模糊效果得到改善。
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