Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques
Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques
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DOI：
10.1088/0266-5611/12/2/004
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发表时间：
1996-04
期刊：
影响因子：
2.1
通讯作者：
M. Hanke;J. Nagy
中科院分区：
文献类型：
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作者：
M. Hanke;J. Nagy
我们考虑了一个给定噪声污染观测的天文成像的病态反卷积问题，以及一个近似已知的卷积核。数学模型的局限性和核函数的形状激发并证明了卷积算子的进一步逼近是自伴随的。这大大简化了重建问题，因为有效的共轭梯度方法现在可以用于真正的未模糊图像的（正则化）近似的迭代计算。由于构造的自伴随算子不能是正定的，因此使用了一种称为MR-II的对称不定共轭梯度技术来避免迭代的崩溃。我们说明了如何使用l曲线方法来停止迭代，并提出了进一步减少计算量的前提条件。
We consider an ill-posed deconvolution problem from astronomical imaging with a given noise-contaminated observation, and an approximately known convolution kernel. The limitations of the mathematical model and the shape of the kernel function motivate and legitimate a further approximation of the convolution operator by one that is self-adjoint. This simplifies the reconstruction problem substantially because the efficient conjugate gradient method can now be used for an iterative computation of a (regularized) approximation of the true unblurred image. Since the constructed self-adjoint operator fails to be positive definite, a symmetric indefinite conjugate gradient technique, called MR-II is used to avoid a breakdown of the iteration. We illustrate how the L-curve method can be used to stop the iterations, and suggest a preconditioner for further reducing the computations.