Abubakar Aria, van den Berg Peter M, Habashy Tarek M, Braunisch Henning
Schlumberger-Doll Research, Ridgefield, CT 06877, USA.
IEEE Trans Image Process. 2004 Nov;13(11):1524-32. doi: 10.1109/tip.2004.836172.
In this work, an iterative inversion algorithm for deblurring and deconvolution is considered. The algorithm is based on the conjugate gradient scheme and uses the so-called weighted L2-norm regularizer to obtain a reliable solution. The regularizer is included as a multiplicative constraint. In this way, the appropriate regularization parameter will be controlled by the optimization process itself. In fact, the misfit in the error in the space of the blurring operator is the regularization parameter. Then, no a priori knowledge on the blurred data or image is needed. If noise is present, the misfit in the error consisting of the blurring operator will remain at a large value during the optimization process; therefore, the weight of the regularization factor will be more significant. Hence, the noise will, at all times, be suppressed in the reconstruction process. Although one may argue that, by including the regularization factor as a multiplicative constraint, the linearity of the problem has been lost, careful analysis shows that, under certain restrictions, no new local minima are introduced. Numerical testing shows that the proposed algorithm works effectively and efficiently in various practical applications.
在这项工作中，考虑了一种用于去模糊和反卷积的迭代反演算法。该算法基于共轭梯度法，并使用所谓的加权L2范数正则化器来获得可靠的解。正则化器作为一个乘法约束被包含在内。通过这种方式，合适的正则化参数将由优化过程本身来控制。实际上，模糊算子空间中误差的失配就是正则化参数。因此，无需关于模糊数据或图像的先验知识。如果存在噪声，在优化过程中，由模糊算子组成的误差中的失配将保持在一个较大的值；因此，正则化因子的权重将更显著。因此，在重建过程中噪声将始终被抑制。尽管有人可能会认为，通过将正则化因子作为乘法约束包含在内，问题的线性已丧失，但仔细分析表明，在某些限制条件下，不会引入新的局部极小值。数值测试表明，所提出的算法在各种实际应用中有效且高效地工作。
