Research in Motion, Waterloo, Ontario, Canada.
IEEE Trans Image Process. 2011 Feb;20(2):405-16. doi: 10.1109/TIP.2010.2070073. Epub 2010 Aug 26.
The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the resolution limitations of an imaging device in use and/or by the destructive influence of measurement noise. Specifically, when the noise obeys a Poisson probability law, standard approaches to the problem of image reconstruction are based upon using fixed-point algorithms which follow the methodology first proposed by Richardson and Lucy. The practice of using these methods, however, shows that their convergence properties tend to deteriorate at relatively high noise levels. Accordingly, in the present paper, a novel method for denoising and/or deblurring of digital images corrupted by Poisson noise is introduced. The proposed method is derived under the assumption that the image of interest can be sparsely represented in the domain of a linear transform. Consequently, a shrinkage-based iterative procedure is proposed, which guarantees the solution to converge to the global maximizer of an associated maximum a posteriori criterion. It is shown in a series of computer-simulated experiments that the proposed method outperforms a number of existing alternatives in terms of stability, precision, and computational efficiency.
从退化的测量值重建数字图像的问题被认为是工程和成像科学各个领域中至关重要的问题。在这种情况下，退化通常是由使用的成像设备的分辨率限制和/或测量噪声的破坏性影响引起的。具体来说，当噪声服从泊松概率定律时，图像重建问题的标准方法基于使用固定点算法，这些算法遵循 Richardson 和 Lucy 首次提出的方法。然而，使用这些方法的实践表明，它们的收敛特性在相对较高的噪声水平下趋于恶化。因此，本文提出了一种用于去除泊松噪声污染的数字图像去噪和/或去模糊的新方法。所提出的方法是在感兴趣的图像可以在线性变换的域中稀疏表示的假设下导出的。因此，提出了一种基于收缩的迭代过程，该过程保证解决方案收敛到相关最大后验准则的全局最大值。在一系列计算机模拟实验中表明，所提出的方法在稳定性、精度和计算效率方面优于许多现有替代方法。
