Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms
Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms
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DOI：
10.1109/83.743855
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发表时间：
1999-02-01
影响因子：
10.6
通讯作者：
Bresler, Y
中科院分区：
文献类型：
--
作者：
Harikumar, G;Bresler, Y
我们解决了通过两个或更多未知的有限脉冲响应（FIR）过滤器恢复图像中图像的问题。我们开发了有关解决方案的存在和独特性的理论结果，并表明在某些一般真实的假设下，过滤器和图像都可以在没有噪声的情况下完全确定，并且在其存在下稳定估计。我们提出有效的算法来估计功能及其大小。这些算法分为两种类型，基于子空间和基于似然的类型，并且是针对在一个维度中多冰道盲解反卷积问题解决方案提出的技术的扩展。我们提出记忆和计算有效的技术，以处理在二维（2-D）情况下产生的非常大的矩阵。一旦确定模糊函数，它们就会在多通道反卷积步骤中使用，以重建未知图像。边缘效应的理论和实际含义以及“弱令人兴奋的”图像被检查，最后，在合成和真实数据上证明了算法。
We address the problem of restoring an image from its noisy convolutions with two or more unknown finite impulse response (FIR) filters. We develop theoretical results about the existence and uniqueness of solutions, and show that under some generically true assumptions, both the filters and the image can he determined exactly in the absence of noise, and stably estimated in its presence. We present efficient algorithms to estimate the blur functions and their sizes. These algorithms are of two types, subspace-based and likelihood-based, and are extensions of techniques proposed for the solution of the multichannel blind deconvolution problem in one dimension. We present memory and computation-efficient techniques to handle the very large matrices arising in the two-dimensional (2-D) case. Once the blur functions are determined, they are used in a multichannel deconvolution step to reconstruct the unknown image. The theoretical and practical implications of edge effects, and "weakly exciting" images are examined, Finally, the algorithms are demonstrated on synthetic and real data.